{"as_of":"2026-07-12T02:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f3500ade1e14458cf1dd472ab775f095a655fea2794bde8397deca216426e0bd","coverage":[{"denominator":46,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":46,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-24T01:43:55.881513Z","state":"measured"},{"denominator":46,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":46,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-07-11T06:31:22.384518+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2404.16004/citation-record","integrity":"/paper/2404.16004/integrity","json":"/paper/2404.16004/citation-record.json","paper":"/paper/2404.16004"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"BI|O = L E B(HI|O,E)","venue":null,"work_id":"ce5944fc-61ff-4e65-a645-bbb4563b488f","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:86bed5afb73113a098c09ad89ef462070f0fb4e53fdfed3c1169f1e498df7903","observation_id":"15d3ec37-41d4-410c-b18e-e4f2e3d3aeb5","resolution":{"observed_at":"2026-05-24T01:45:56.092077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"9c14711f-b21e-4935-87e9-7e635aca9246","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:a0f25e5ea33aa505a5fe7f67364468469221ad85f3c1051b20b5e1782b321d3f","observation_id":"3df029e9-d8ac-4d20-a516-9dd2abbd4562","resolution":{"observed_at":"2026-05-24T01:45:56.116894Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"236cf93f-f4c9-4c97-bbc4-b4b29989433e","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:2488570a74b547d861ded5884f16dd74908dce2659822fe3ab08caf946995e02","observation_id":"c99fecb5-869c-48db-b68a-174497d27c0e","resolution":{"observed_at":"2026-05-24T01:45:56.141604Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Σ( X) = Xρ tI","venue":null,"work_id":"e918ae9b-bb71-45b0-8d50-9ef82a03331c","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:1796b563a2d97b119947ce3652d0edeea15011157556f7353a007980f96d4916","observation_id":"f97384ac-1a83-4464-9bc4-027a4dba0f4a","resolution":{"observed_at":"2026-05-24T01:45:56.137185Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"29d53099-7ba8-423d-92a5-5ca3796e42fc","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:279fc06824a124027bb2dc0e52124d49676ac9152eaf2c7517cd2fc88c76beea","observation_id":"2e845a49-a2df-454b-9723-8e8bff06efdf","resolution":{"observed_at":"2026-05-24T01:45:56.103922Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Trace preservation is just the property TrBE OE[ρE,E] = IIE DIE cE = DIE K","venue":null,"work_id":"4cf1dd12-735e-4289-8328-83dc2ab3f773","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:67ebd23012db285abab437c92ac599ed6b67105c6ef171528177ef819c4fafb1","observation_id":"dc7fb9ec-092e-40ba-8c66-295f36ca0265","resolution":{"observed_at":"2026-05-24T01:45:56.146105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"This can be generalised to density matrices in the folium of a state ω ∈ S (A) of some C*-algebra","venue":null,"work_id":"bfc2c9ee-a480-413c-883b-832b780c4fe1","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:43c3a9eca95a5592a88eca7c243bd4ca65d3179f98f0bfc3799fa68ab67d7041","observation_id":"b1dacbfb-b24a-4427-943d-63b4891994f3","resolution":{"observed_at":"2026-05-24T01:45:56.132983Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"They may be generalised to approx- imate identities of C*-algebras and associated nets of approximate extension maps","venue":null,"work_id":"303c7104-c84b-4695-9f90-f0e3bbe0e9ea","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:0769b94b4fe8fa7de4b11036541e4cb3cc72bea65ab07232d6765aa5b6ee06d2","observation_id":"a7dbcc18-5432-4e33-9483-b38ef6b6a377","resolution":{"observed_at":"2026-05-24T01:45:56.099709Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Relative to an extension map, one may either take the inverse or the adjoint generalisation","venue":null,"work_id":"d8c1a80e-16b7-4fc4-bb62-409eadb7c1c0","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:dfbaaed41d73c59805d235ba492569fff537447c664735bbd4040f0e5b7eeb6f","observation_id":"25663ac4-3a4f-4b9c-b6f7-b107c620a96f","resolution":{"observed_at":"2026-05-24T01:45:56.108254Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Our example fits directly into a small class of maps in the general scheme which can be represented by a density matrix ρ","venue":null,"work_id":"cf8699c6-3500-4303-a1ff-eeee699ab7a9","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:d46c3cbd8f5e20349368f4e7c8377ca38ee02a85421bf6f52d3e84c7afb5922c","observation_id":"90e6de0d-0b11-41a3-a5fc-7e470d6aced0","resolution":{"observed_at":"2026-05-24T01:45:56.128196Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Channel-state duality","venue":null,"work_id":"2834277c-5839-4a50-b9d5-0a9a746a69bb","year":2013},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:9f04ba6c3a097025c2ad4c8a1d95d2d55d403f6e39b4e57c426692bdb4a1ce5a","observation_id":"fe325ec6-d6c6-472e-86f5-e1bdb077403f","resolution":{"observed_at":"2026-05-24T01:45:56.120675Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Channel-state duality","venue":null,"work_id":"ce5e5d68-9c7f-4e0f-8216-b305ff6c38fd","year":2013},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:cf841f165faafab7ba7c1b04709071eb7f1d5a2d8af0ccd56b8273d8f040d339","observation_id":"ea58caf0-6715-431c-8430-beb34b5b2a59","resolution":{"observed_at":"2026-05-24T01:45:56.124412Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On quan- tum operations as quantum states","venue":null,"work_id":"7d053866-32f9-49a7-b26c-2f5bfa6ea407","year":2004},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:93aa3cd7935df279e6a33970f3483f0f0b83502c67de0bd558c9608baac226bd","observation_id":"83c178d1-1fae-45f0-8e51-06bf0f0a95f6","resolution":{"observed_at":"2026-05-24T01:45:56.112958Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2207.07625","last_updated":"2024-02-26T19:40:48Z","snapshot_observed_at":"2026-07-06T13:31:50.015965Z","submitted_at":"2022-07-15T17:37:47Z","title":"Holographic properties of superposed quantum geometries","version":3},"cited_work":{"arxiv_id":"2207.07625","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2207.07625","snapshot_observed_at":"2026-06-30T15:44:48.695991Z","title":"Holographic properties of superposed quantum geometries","venue":null,"work_id":"db4b46a2-f7f1-4762-9247-9c0f77ec51b7","year":2024},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/2207.07625","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:011c6c747580ff09f99195c008f666f59126fb34274228f5cf45bd345ddde698","observation_id":"c5532c99-2721-434d-b6b9-ddfdb5948d31","resolution":{"observed_at":"2026-05-24T01:45:55.650523Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1601.01694","last_updated":"2016-10-17T17:50:50Z","snapshot_observed_at":"2026-07-06T04:42:11.317805Z","submitted_at":"2016-01-07T21:00:25Z","title":"Holographic duality from random tensor networks","version":3},"cited_work":{"arxiv_id":"1601.01694","doi":null,"metadata_source":"pith","pith_arxiv_id":"1601.01694","snapshot_observed_at":"2026-07-04T06:49:38.957660Z","title":"Holographic duality from random tensor networks","venue":"hep-th","work_id":"5fcf4f7e-805a-491c-adf2-a9a0fb012d28","year":2016},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/1601.01694","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:98ebc05c99e16fe78dd428796ee5252cd3d4a8bc9e2d0267a27e24dd55284a56","observation_id":"7b428503-726d-4e13-a553-7e7f63e8d78c","resolution":{"observed_at":"2026-05-24T01:45:55.655639Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.06436","last_updated":"2023-09-12T17:56:02Z","snapshot_observed_at":"2026-07-06T16:17:34.799881Z","submitted_at":"2023-09-12T17:56:02Z","title":"Holographic Tensor Networks with Bulk Gauge Symmetries","version":1},"cited_work":{"arxiv_id":"2309.06436","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2309.06436","snapshot_observed_at":"2026-06-30T15:44:48.730323Z","title":"Holographic tensor networks with bulk gauge symmetries","venue":null,"work_id":"5858ebea-ebee-4289-b4c3-848de813cfac","year":2024},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/2309.06436","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:56e4947923bf096e4f88f271e48bc7bdcee0a3b2cd814dc2407ebc105c4dd618","observation_id":"a40370f3-69a2-48d8-a97f-4ecfaf617bd7","resolution":{"observed_at":"2026-05-24T01:45:55.644229Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspon- dence","venue":null,"work_id":"e97ba736-41db-4c65-b870-fd23fb4a616e","year":2015},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:b34b800365f6178ccf57ebc8219aa2f9f647c3190747df2ad6074c670c97734d","observation_id":"0fab3c08-fc2b-4e10-b593-0b404d927fa1","resolution":{"observed_at":"2026-05-24T01:45:56.081546Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1503.06237","last_updated":"2015-07-22T01:31:24Z","snapshot_observed_at":"2026-07-06T04:12:41.179125Z","submitted_at":"2015-03-20T21:56:06Z","title":"Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence","version":2},"cited_work":{"arxiv_id":"1503.06237","doi":null,"metadata_source":"pith","pith_arxiv_id":"1503.06237","snapshot_observed_at":"2026-07-10T03:26:44.511669Z","title":"Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence","venue":"hep-th","work_id":"8091ef6f-b8f8-44ac-aa9c-8106d97fa41c","year":2015},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/1503.06237","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:e57ea5aa37987e3904bf17537b086b3da9e5488a57b275391728c40df16d09f3","observation_id":"0d99f40b-852e-4247-b3d9-d828b9aff9e0","resolution":{"observed_at":"2026-05-24T01:45:55.638837Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1109.0036","last_updated":"2012-04-26T16:39:42Z","snapshot_observed_at":"2026-07-06T02:33:15.517861Z","submitted_at":"2011-08-31T21:04:03Z","title":"Decomposition of entanglement entropy in lattice gauge theory","version":2},"cited_work":{"arxiv_id":"1109.0036","doi":null,"metadata_source":"pith","pith_arxiv_id":"1109.0036","snapshot_observed_at":"2026-07-03T12:48:12.244382Z","title":"Decomposition of entanglement entropy in lattice gauge theory","venue":"hep-th","work_id":"94445647-df6c-4f74-a3d9-d1170f1f671a","year":2011},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/1109.0036","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:f4ab981e62b76ca6e1d42a78c05554bc15dab76051bf1266e34d2b0b97fbcfa0","observation_id":"16636a84-3cfa-44e6-a7a3-08414087ece2","resolution":{"observed_at":"2026-05-24T01:45:55.599120Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Corner symmetry and quantum geometry, February","venue":null,"work_id":"3e928ea3-d34f-41b0-b7b5-c9276deba50f","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:e32eb8df8551ee8dd02266781591a74e333c004e1489e95fdaff8fbb421ee772","observation_id":"41893108-b140-415b-83f5-1d60eff706c6","resolution":{"observed_at":"2026-05-24T01:45:56.078761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2302.12799","last_updated":"2023-04-09T20:36:02Z","snapshot_observed_at":"2026-07-06T14:55:34.311264Z","submitted_at":"2023-02-24T18:22:34Z","title":"Corner symmetry and quantum geometry","version":2},"cited_work":{"arxiv_id":"2302.12799","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2302.12799","snapshot_observed_at":"2026-07-02T14:47:04.529785Z","title":"Freidel, M","venue":null,"work_id":"618a1d25-6e3b-44d9-8233-c7656c86c149","year":2024},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/2302.12799","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:9ac5fc8b8bf8da6ded4eb90d4517bc09523c8e9ae2d64d8fda01931ac8c9a9a6","observation_id":"15058a95-301f-47f6-8d08-dfd0e660f2c1","resolution":{"observed_at":"2026-05-24T01:45:55.596038Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2302.05922","last_updated":"2023-02-12T14:29:25Z","snapshot_observed_at":"2026-07-06T14:50:56.751281Z","submitted_at":"2023-02-12T14:29:25Z","title":"Loop Quantum Gravity and Quantum Information","version":1},"cited_work":{"arxiv_id":"2302.05922","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2302.05922","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"122c10fc-c633-435b-b8aa-c8c45061069c","year":2023},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/2302.05922","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:9f3bf88b7e3aa2093afc82dc771b078766ff65299ece33b13f4800e1fa84b663","observation_id":"7c6199dd-a88b-43d8-9674-f9ffe7af5b2d","resolution":{"observed_at":"2026-05-24T01:45:55.613897Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"03f7b4c7-982d-4319-99e9-8eab3b898d5b","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:263393f280efbe62f090d5917b959b871a2e3c3a4831018e0e72c4544a1c2024","observation_id":"cf48a5f3-ea0c-47fc-84a7-96fce3a0b5aa","resolution":{"observed_at":"2026-05-24T01:45:56.041432Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"42509312-b47a-470c-9627-2e4267e351ab","year":2015},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:4643926cacdfe7e28e888e204f9779190255f5c8e27485860509c99cbbe0890f","observation_id":"8e04e939-a9b3-461f-acef-ac5010dab5fb","resolution":{"observed_at":"2026-05-24T01:45:56.033451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Comments on Defining Entanglement Entropy, September","venue":null,"work_id":"837e54c7-2ce3-4570-8105-d352900211f1","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:e734744ebe90a0777368fa4e1276d32afb413dfd6b987625b9d7b581fa8a0dff","observation_id":"766e0a10-cf34-4377-8fcb-057499a8f81d","resolution":{"observed_at":"2026-05-24T01:45:56.066194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1808.05939","last_updated":"2018-09-16T15:17:56Z","snapshot_observed_at":"2026-07-06T06:56:10.641252Z","submitted_at":"2018-08-17T17:43:58Z","title":"Comments on Defining Entanglement Entropy","version":2},"cited_work":{"arxiv_id":"1808.05939","doi":null,"metadata_source":"pith","pith_arxiv_id":"1808.05939","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Comments on Defining Entanglement Entropy","venue":"hep-th","work_id":"0f996742-f394-4119-8384-b39fe89e0566","year":2018},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/1808.05939","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:cf3cffd483c855c85baa409454f5e71b05a16a870dead3093e370ffa5bea0b7b","observation_id":"6611cf59-b1cc-45e2-bc2a-cd6f0bbdb7ad","resolution":{"observed_at":"2026-05-24T01:45:55.627769Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1507.02573","last_updated":"2015-07-09T16:02:41Z","snapshot_observed_at":"2026-07-06T04:23:21.529552Z","submitted_at":"2015-07-09T16:02:41Z","title":"Quantum gravity at the corner","version":1},"cited_work":{"arxiv_id":"1507.02573","doi":null,"metadata_source":"pith","pith_arxiv_id":"1507.02573","snapshot_observed_at":"2026-07-02T14:47:04.501571Z","title":"Quantum gravity at the corner","venue":"gr-qc","work_id":"ce2698db-981a-4956-bbee-85b5a2313f39","year":2015},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/1507.02573","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:9626eba4cca6aca20263b86a082c9b8693eb745a04aa9e96a9985bfca963b1d9","observation_id":"e346e2dc-1a6d-4e99-8a98-c16daaebd89c","resolution":{"observed_at":"2026-05-24T01:45:55.619283Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The Theory of Quantum Information","venue":null,"work_id":"7b98254b-b2fc-4033-8932-934a4072a0ba","year":2018},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:ff88ea370aab5a9145b91ceb86015d6947404aeaa749aade69371acb7b2cd7ec","observation_id":"cb94c832-0274-4a1e-b617-eabcbc809b2f","resolution":{"observed_at":"2026-05-24T01:45:56.054147Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1511.02671","last_updated":"2015-12-25T16:59:54Z","snapshot_observed_at":"2026-07-06T04:35:49.333626Z","submitted_at":"2015-11-09T13:23:39Z","title":"Entanglement with Centers","version":3},"cited_work":{"arxiv_id":"1511.02671","doi":null,"metadata_source":"pith","pith_arxiv_id":"1511.02671","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Entanglement with Centers","venue":"hep-th","work_id":"c68057a1-cb82-4b27-9a8d-c5e9d04d160c","year":2015},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/1511.02671","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:071b625908a5022d093bb89ae1dcebe7a9000a129bd98ab0a5a929bf5e6d44d5","observation_id":"a6cb2380-316e-478f-ab19-4b5f0f6e3e9a","resolution":{"observed_at":"2026-05-24T01:45:55.584944Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"ph/0103030","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Virtual Quantum Subsystems","venue":null,"work_id":"0bc914de-4beb-4099-9933-a1a0963a4d40","year":2001},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:c9d2cd9fb9ccd6d7acbbd80b34e5f748ae94f56ec4f6e467bacbff04a3ce9792","observation_id":"233935db-7879-46f0-b22b-d66c86b897d8","resolution":{"observed_at":"2026-05-24T01:45:55.633712Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1702.04924","last_updated":"2018-05-14T10:51:41Z","snapshot_observed_at":"2026-07-06T05:30:15.848977Z","submitted_at":"2017-02-16T11:17:35Z","title":"Entanglement measures and their properties in quantum field theory","version":3},"cited_work":{"arxiv_id":"1702.04924","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1702.04924","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Entanglement measures and their properties in quantum field theory, May 2018","venue":null,"work_id":"ec3dec2f-90d7-4530-85b9-939b9ab8c1b6","year":2018},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/1702.04924","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:45fd30ff0f29673e28e39ce0665cc372b69f6c05461da2d81da8ec13603c8154","observation_id":"50cd8a4f-b082-462b-ab6c-89a7f48e4830","resolution":{"observed_at":"2026-05-24T01:45:55.561253Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"9ac61e20-138e-4a9e-b7f1-40e44aeddf18","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:c771c485cf6023db9b7af47fa1fdaaad7f3f16bb23401d0c7d7bbce6c180acbb","observation_id":"2e8409d1-fa74-49f7-9511-3819e21811f3","resolution":{"observed_at":"2026-05-24T01:45:56.050088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"c0f90f26-acbf-47fb-9456-5b0ff54d64a4","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:b7a1bea5d1c87605b11dd1d595ffc65f4a0ae7bb31f93bf4cb91d87961ea5ef8","observation_id":"66e42d0b-6937-4d4f-a84d-96cccc187618","resolution":{"observed_at":"2026-05-24T01:45:56.073716Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d1e62d42-8cd6-4290-86dc-d04262589087","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:c11ea8cbd8fe6b456f8f3e1f71d4a3eb73f7b3d29774fda3d3bee64196fa3031","observation_id":"95bd93aa-f17e-4b84-bea7-7adb5c790815","resolution":{"observed_at":"2026-05-24T01:45:56.062172Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1312.1183","last_updated":"2013-12-04T14:38:00Z","snapshot_observed_at":"2026-07-06T03:29:57.805699Z","submitted_at":"2013-12-04T14:38:00Z","title":"Remarks on entanglement entropy for gauge fields","version":1},"cited_work":{"arxiv_id":"1312.1183","doi":null,"metadata_source":"pith","pith_arxiv_id":"1312.1183","snapshot_observed_at":"2026-07-10T03:26:44.483384Z","title":"Remarks on entanglement entropy for gauge fields","venue":"hep-th","work_id":"5067052b-8b15-48ee-92e1-eee6cc7e7df0","year":2013},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/1312.1183","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:93dc1ffe81408e2e41b94e2afb5e3f97d8379cae224edd78d1e8f78a83a8c505","observation_id":"8fa14202-77e4-4dc8-b2fc-3bec932b8f46","resolution":{"observed_at":"2026-05-24T01:45:55.594032Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1904.08370","last_updated":"2019-11-18T15:36:36Z","snapshot_observed_at":"2026-07-06T07:46:48.062902Z","submitted_at":"2019-04-17T17:11:43Z","title":"Typical entanglement entropy in the presence of a center: Page curve and its variance","version":3},"cited_work":{"arxiv_id":"1904.08370","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1904.08370","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Typical entropy of a subsystem: P age curve and its variance","venue":null,"work_id":"5018b49b-e76f-4b88-8593-de506d6d4516","year":1904},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/1904.08370","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:760021a1bcc89b24404ba5f6ceb98bfca3abe59d307d8ba5f77ec4889b7daaaa","observation_id":"a43c207f-01a6-4764-8913-bc495674e641","resolution":{"observed_at":"2026-05-24T01:45:55.590213Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d8e9ac78-a038-4ca3-b018-7042361a954e","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:afa8833bf2a9f5476cc62a888c29d1059e5ce36f3eac24c8454ac32088a47968","observation_id":"16ae23b8-6bc5-4282-93d9-4c74042540de","resolution":{"observed_at":"2026-05-24T01:45:56.084733Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"74f3063e-73c2-4aae-8995-c76bbd3492a4","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:fda21d432fae9cca81a1251b723f82a573c99d8b583e9092fd88143befb45c02","observation_id":"4d9ea9d0-8e9a-4bd2-96b9-575f08cd5b0a","resolution":{"observed_at":"2026-05-24T01:45:56.057939Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1212.0248","last_updated":"2012-12-07T18:43:56Z","snapshot_observed_at":"2026-07-06T03:01:07.290375Z","submitted_at":"2012-12-02T21:26:38Z","title":"The structure of Renyi entropic inequalities","version":2},"cited_work":{"arxiv_id":"1212.0248","doi":null,"metadata_source":"pith","pith_arxiv_id":"1212.0248","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The structure of Renyi entropic inequalities","venue":"quant-ph","work_id":"0598648c-2bd2-4a03-8a62-8e72063b3f00","year":2012},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/1212.0248","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:5f2334b839f97752bb58e236a69cc105228ef14b5e6a4e6a0807f35f21ca254f","observation_id":"e033d647-39b3-47d3-ad8e-dad00b21a153","resolution":{"observed_at":"2026-05-24T01:45:55.572922Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"These have a known expres- sion and satisfy nice properties as an analogue of the von Neumann mutual information","venue":null,"work_id":"7ba999e7-4a8c-441d-8114-110bc9435e3b","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:9b6de4892ab94b6c3f4d139c3cb2427181d2e9492f689d8ee8414133138c254c","observation_id":"32a54f1c-7b96-496f-9b3a-5b7c3530829d","resolution":{"observed_at":"2026-05-24T01:45:56.070271Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1909.13309","last_updated":"2020-05-04T23:06:48Z","snapshot_observed_at":"2026-07-06T08:25:31.468271Z","submitted_at":"2019-09-29T16:30:58Z","title":"Channel-state duality and the separability problem","version":2},"cited_work":{"arxiv_id":"1909.13309","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1909.13309","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"77cee26d-9028-4cfb-b883-8044f6e10346","year":2020},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/1909.13309","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:1397b5f7fc37a6205ded301463f19b288f1104cec8c6202efcf8805e24b53835","observation_id":"2ff33b6d-6aab-49d3-9288-7fcb5401287b","resolution":{"observed_at":"2026-05-24T01:45:55.601464Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"qc/9305007","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Average entropy of a subsystem","venue":null,"work_id":"21b36c09-9408-44a6-835a-48dd73857884","year":1993},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:f5c8eedfeb9cb69c5c2374a3a7f1ee5efd20364ec92d91ff2c7592903ee5c09b","observation_id":"dc390880-212c-433a-a70d-7a49834a60c6","resolution":{"observed_at":"2026-05-24T01:45:55.607680Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"59f79279-e2d0-40d4-8d77-b12543f3559f","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:ccb5f2ee5f861cd79f5f990ff6be64be35da17b1ef7c80cc67fe725e201b2952","observation_id":"8e3aa349-8b60-4c36-9b61-aa8034fb4295","resolution":{"observed_at":"2026-05-24T01:45:56.045607Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d52eee01-a668-4e1b-9b7d-06d4c9384528","year":null},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:7699a9d8165587cef01293696e8415a3894ef9e231df94df4355ed5f56d37710","observation_id":"877dc04e-0acc-40af-93f2-61df8d4f7955","resolution":{"observed_at":"2026-05-24T01:45:56.077706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On trace class operators (and Hilbert- Schmidt operators)","venue":null,"work_id":"2d6dbba5-5511-468a-8140-824b018fb2a4","year":2022},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:a7557e818f6496927e57a7e4c754f79b08463646825941495cb566aaf4ed2bd2","observation_id":"e61d6874-34a7-4574-b797-7c82ccaeba1e","resolution":{"observed_at":"2026-05-24T01:45:56.088442Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2103.01709","last_updated":"2021-09-04T13:36:28Z","snapshot_observed_at":"2026-07-06T10:46:01.808404Z","submitted_at":"2021-03-02T13:33:42Z","title":"Computable R\\'enyi mutual information: Area laws and correlations","version":2},"cited_work":{"arxiv_id":"2103.01709","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2103.01709","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Scalet, Alvaro M","venue":null,"work_id":"e0dab5bb-66c9-4900-bb5e-6aa9f1b9d2cb","year":2021},"citing_paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-05-24T01:43:55.881513Z"},"links":{"cited_paper":"/paper/2103.01709","citing_paper":"/paper/2404.16004"},"observation_digest":"sha256:84e5f4df8ac2998f415d3daceb111f069bb1de6f24dd4847a0451945eda0c3d9","observation_id":"a4a58619-a0a9-43d8-a387-838c44ba15cd","resolution":{"observed_at":"2026-05-24T01:45:55.580055Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2404.16004","last_updated":"2024-11-05T00:55:03Z","latest_version":2,"primary_category":"quant-ph","snapshot_observed_at":"2026-07-06T18:05:03.284784Z","submitted_at":"2024-04-24T17:35:02Z","title":"Channel-State duality with centers"},"reference_resolution":{"displayed":46,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":18,"verified_fuzzy":28},"total_outbound_references":46},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"thesis":"As of 12 July 2026, this Paper Citation Record lists 46 of 46 outbound references and 0 inbound Pith citation observations for arXiv:2404.16004."}