{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JFUFJQKG5AWMCH7RAYYF5AHCMD","short_pith_number":"pith:JFUFJQKG","canonical_record":{"source":{"id":"1508.03886","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-08-17T00:38:40Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"ad1cfb0b9752155afaee8ef54f17248ecf7f3155b598fa31e8f8d58794f8d457","abstract_canon_sha256":"f8dfee4e2eda1beb1fbb518e1b2d39b343c914c84f841deb288c2cc8ed1c6c51"},"schema_version":"1.0"},"canonical_sha256":"496854c146e82cc11ff106305e80e260e292cb03876d2aba0795f3bba07442b5","source":{"kind":"arxiv","id":"1508.03886","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03886","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03886v2","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03886","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"JFUFJQKG5AWM","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JFUFJQKG5AWMCH7R","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JFUFJQKG","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JFUFJQKG5AWMCH7RAYYF5AHCMD","target":"record","payload":{"canonical_record":{"source":{"id":"1508.03886","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-08-17T00:38:40Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"ad1cfb0b9752155afaee8ef54f17248ecf7f3155b598fa31e8f8d58794f8d457","abstract_canon_sha256":"f8dfee4e2eda1beb1fbb518e1b2d39b343c914c84f841deb288c2cc8ed1c6c51"},"schema_version":"1.0"},"canonical_sha256":"496854c146e82cc11ff106305e80e260e292cb03876d2aba0795f3bba07442b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:08.203522Z","signature_b64":"OCeYqe9/vyPzDPh0yBuVMBzVOx04uMt4OuhbAbqE6sb/SIbmHt1M8f7uXaCo1l8poHgLv0HYBFYJ514MzCtgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"496854c146e82cc11ff106305e80e260e292cb03876d2aba0795f3bba07442b5","last_reissued_at":"2026-05-18T01:23:08.203013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:08.203013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.03886","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"etj2HUljRR7CY0k1ftb3eTBYyPQJNQhz5MlAXdQaiJWQllUlawDrFzNC6QgE0iG61mJWIFs8SCAjTobm9vZhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:25:55.438448Z"},"content_sha256":"a54e1b78142043b28ad597698446bc69ab321f8c73e675260e739977de37fb07","schema_version":"1.0","event_id":"sha256:a54e1b78142043b28ad597698446bc69ab321f8c73e675260e739977de37fb07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JFUFJQKG5AWMCH7RAYYF5AHCMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometry of reduced density matrices for symmetry-protected topological phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"Bei Zeng, Ji-Yao Chen, Yi Shen, Zhengfeng Ji, Zheng-Xin Liu","submitted_at":"2015-08-17T00:38:40Z","abstract_excerpt":"In this paper, we study the geometry of reduced density matrices for states with symmetry-protected topological (SPT) order. We observe ruled surface structures on the boundary of the convex set of low dimension projections of the reduced density matrices. In order to signal the SPT order using ruled surfaces, it is important that we add a symmetry-breaking term to the boundary of the system---no ruled surface emerges in systems without boundary or when we add a symmetry-breaking term representing a thermodynamic quantity. Although the ruled surfaces only appear in the thermodynamic limit wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03886","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0t7r9bsvVPXNFlDvhIa9Xdwb4M2R5HolyZif/eht5X3+HluHSDuGsOLZpZPIiz1nOhhjUus8jFzzQjVuEd10Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:25:55.438829Z"},"content_sha256":"16c698d6446d693c158fa7c2105769867ea3298d42ee0361c7b60f8dc5ec4b46","schema_version":"1.0","event_id":"sha256:16c698d6446d693c158fa7c2105769867ea3298d42ee0361c7b60f8dc5ec4b46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JFUFJQKG5AWMCH7RAYYF5AHCMD/bundle.json","state_url":"https://pith.science/pith/JFUFJQKG5AWMCH7RAYYF5AHCMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JFUFJQKG5AWMCH7RAYYF5AHCMD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T04:25:55Z","links":{"resolver":"https://pith.science/pith/JFUFJQKG5AWMCH7RAYYF5AHCMD","bundle":"https://pith.science/pith/JFUFJQKG5AWMCH7RAYYF5AHCMD/bundle.json","state":"https://pith.science/pith/JFUFJQKG5AWMCH7RAYYF5AHCMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JFUFJQKG5AWMCH7RAYYF5AHCMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JFUFJQKG5AWMCH7RAYYF5AHCMD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f8dfee4e2eda1beb1fbb518e1b2d39b343c914c84f841deb288c2cc8ed1c6c51","cross_cats_sorted":["cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-08-17T00:38:40Z","title_canon_sha256":"ad1cfb0b9752155afaee8ef54f17248ecf7f3155b598fa31e8f8d58794f8d457"},"schema_version":"1.0","source":{"id":"1508.03886","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03886","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03886v2","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03886","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"JFUFJQKG5AWM","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JFUFJQKG5AWMCH7R","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JFUFJQKG","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:16c698d6446d693c158fa7c2105769867ea3298d42ee0361c7b60f8dc5ec4b46","target":"graph","created_at":"2026-05-18T01:23:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study the geometry of reduced density matrices for states with symmetry-protected topological (SPT) order. We observe ruled surface structures on the boundary of the convex set of low dimension projections of the reduced density matrices. In order to signal the SPT order using ruled surfaces, it is important that we add a symmetry-breaking term to the boundary of the system---no ruled surface emerges in systems without boundary or when we add a symmetry-breaking term representing a thermodynamic quantity. Although the ruled surfaces only appear in the thermodynamic limit wher","authors_text":"Bei Zeng, Ji-Yao Chen, Yi Shen, Zhengfeng Ji, Zheng-Xin Liu","cross_cats":["cond-mat.str-el"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-08-17T00:38:40Z","title":"Geometry of reduced density matrices for symmetry-protected topological phases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03886","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a54e1b78142043b28ad597698446bc69ab321f8c73e675260e739977de37fb07","target":"record","created_at":"2026-05-18T01:23:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f8dfee4e2eda1beb1fbb518e1b2d39b343c914c84f841deb288c2cc8ed1c6c51","cross_cats_sorted":["cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-08-17T00:38:40Z","title_canon_sha256":"ad1cfb0b9752155afaee8ef54f17248ecf7f3155b598fa31e8f8d58794f8d457"},"schema_version":"1.0","source":{"id":"1508.03886","kind":"arxiv","version":2}},"canonical_sha256":"496854c146e82cc11ff106305e80e260e292cb03876d2aba0795f3bba07442b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"496854c146e82cc11ff106305e80e260e292cb03876d2aba0795f3bba07442b5","first_computed_at":"2026-05-18T01:23:08.203013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:08.203013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OCeYqe9/vyPzDPh0yBuVMBzVOx04uMt4OuhbAbqE6sb/SIbmHt1M8f7uXaCo1l8poHgLv0HYBFYJ514MzCtgBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:08.203522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03886","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a54e1b78142043b28ad597698446bc69ab321f8c73e675260e739977de37fb07","sha256:16c698d6446d693c158fa7c2105769867ea3298d42ee0361c7b60f8dc5ec4b46"],"state_sha256":"14e29e636628720e692f82ef6cb6f7079c43f3ef2ab2dab4de35789abf451155"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T0e6KEW237olGqSNepCP38k72yLK67VO03mpkAnnONV9qafti+4IZehLiy6ffgmLNkxPwE4jinfOKoYqmKxBAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:25:55.441625Z","bundle_sha256":"b3cebdbc4a1f50f4bece2bb34efe31a840789750b6d0e8001dd1aa209683c08e"}}