{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:46XFAD7AIRY37Q3U5VUQULYLUC","short_pith_number":"pith:46XFAD7A","canonical_record":{"source":{"id":"2605.13014","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T05:08:52Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"bd5522dd2cb463f144f707ae489d644b0a5923d4ee0abcdffa07573d5400da3f","abstract_canon_sha256":"b52cc305ec75d6729fdcb9cf4291ed20ab0008b8d717a4b27f23832427609b46"},"schema_version":"1.0"},"canonical_sha256":"e7ae500fe04471bfc374ed690a2f0ba09340e70e65e172020fbe138e4b1cd047","source":{"kind":"arxiv","id":"2605.13014","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13014","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13014v1","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13014","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"pith_short_12","alias_value":"46XFAD7AIRY3","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"46XFAD7AIRY37Q3U","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"46XFAD7A","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:46XFAD7AIRY37Q3U5VUQULYLUC","target":"record","payload":{"canonical_record":{"source":{"id":"2605.13014","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T05:08:52Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"bd5522dd2cb463f144f707ae489d644b0a5923d4ee0abcdffa07573d5400da3f","abstract_canon_sha256":"b52cc305ec75d6729fdcb9cf4291ed20ab0008b8d717a4b27f23832427609b46"},"schema_version":"1.0"},"canonical_sha256":"e7ae500fe04471bfc374ed690a2f0ba09340e70e65e172020fbe138e4b1cd047","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:00.190969Z","signature_b64":"tavDEtlyNNJmq1MgSTToAkLNSP56LjjcedEpiPR+3a+PY6ckmm04TjAvKp1ucXjK95x6Yh62NB8xu/9E7iXgDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7ae500fe04471bfc374ed690a2f0ba09340e70e65e172020fbe138e4b1cd047","last_reissued_at":"2026-05-18T03:09:00.189969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:00.189969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.13014","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:09:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ZpBFafazHTW68uaWCtXNQ108FpnQhY5G5Nc7IVC0neSUjpXTkYkOZgShchvgP1itzvZtnHJpkLE/ZTpQosiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:37:15.122999Z"},"content_sha256":"41c50c1b96c65f459298a75d0bace0da6f1b797ebe7956a6632dce912fc1c1b1","schema_version":"1.0","event_id":"sha256:41c50c1b96c65f459298a75d0bace0da6f1b797ebe7956a6632dce912fc1c1b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:46XFAD7AIRY37Q3U5VUQULYLUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unitary invariance of Connes spectral distances of quantum states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Connes spectral distances between quantum states remain unchanged under unitary transformations in finite spectral triples.","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Bing-Sheng Lin, Ji-Hong Wang, Zhi-Kang You","submitted_at":"2026-05-13T05:08:52Z","abstract_excerpt":"In this paper, we study the properties of Connes spectral distances between quantum states under unitary transformations. We mainly focus on spectral triples with matrix algebras acting on finite dimensional Hilbert spaces via some linear representations. We derive some elementary properties of the Connes spectral distances and optimal elements. We prove that there are some finite spectral triples in which the Lipschitz seminorms are equal to the operator norms. We also explicitly construct some spectral triples in which the Connes spectral distances between quantum states are exactly the quan"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We also explicitly construct some spectral triples in which the Connes spectral distances between quantum states are exactly the quantum trace distances.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the chosen finite-dimensional matrix algebra representations and spectral triples are sufficient to capture the relevant geometric and distance properties of general quantum states.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Connes spectral distances are unitarily invariant and can be constructed to equal quantum trace distances in certain finite spectral triples.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Connes spectral distances between quantum states remain unchanged under unitary transformations in finite spectral triples.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"19e06523161519df9b56e42f2b14a581c6d61c43194b879eac265aa3c71bf45b"},"source":{"id":"2605.13014","kind":"arxiv","version":1},"verdict":{"id":"bfa40eaf-90a8-4e1e-8df5-b61fce1a0106","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:28:44.534952Z","strongest_claim":"We also explicitly construct some spectral triples in which the Connes spectral distances between quantum states are exactly the quantum trace distances.","one_line_summary":"Connes spectral distances are unitarily invariant and can be constructed to equal quantum trace distances in certain finite spectral triples.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the chosen finite-dimensional matrix algebra representations and spectral triples are sufficient to capture the relevant geometric and distance properties of general quantum states.","pith_extraction_headline":"Connes spectral distances between quantum states remain unchanged under unitary transformations in finite spectral triples."},"references":{"count":24,"sample":[{"doi":"","year":1994,"title":"Connes,Noncommutative geometry(Academic Press, New York, 1994)","work_id":"c6460f40-a7e8-4261-9f5a-57eb16730d75","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1989,"title":"Compact metric spaces, Fredholm modules and hyperfinite- ness","work_id":"25046f91-8454-44c5-bd0c-2b7ac6793c8c","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1994,"title":"Distances on a lattice from non- commutative geometry","work_id":"5185bd04-3e82-47dd-ab43-25c6a932aa3e","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2001,"title":"Connes’ distance of one-dimensional lattices: general cases","work_id":"aa38e3ce-7b6d-4922-9d1c-f4928ee56fa6","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"The spectral dis- tance on the Moyal plane","work_id":"16602d11-fccc-4a42-949e-66602e4909d9","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":24,"snapshot_sha256":"0b5554615f198a2f6e5060bedaef8d9b918d31afa39aff468661d34211d72390","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8798b455b0bae44f1e684c18cfb6981c43ee198348776c4a8017e3318cb521b1"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"bfa40eaf-90a8-4e1e-8df5-b61fce1a0106"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:09:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HvUKJfDwQKIaNCwonzBSMtkIq52FhD3NAr7oGzpzJS9HChJQZkzmPwHQqd/HlMAXSiLx8LLBJcEY0CNd2xM8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:37:15.124098Z"},"content_sha256":"562dd3a54d541e627fa34e7560e3acf8f8a0126d2f392e3f9568ceb827cc7d78","schema_version":"1.0","event_id":"sha256:562dd3a54d541e627fa34e7560e3acf8f8a0126d2f392e3f9568ceb827cc7d78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/46XFAD7AIRY37Q3U5VUQULYLUC/bundle.json","state_url":"https://pith.science/pith/46XFAD7AIRY37Q3U5VUQULYLUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/46XFAD7AIRY37Q3U5VUQULYLUC/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":"2026-05-26T22:37:15Z","links":{"resolver":"https://pith.science/pith/46XFAD7AIRY37Q3U5VUQULYLUC","bundle":"https://pith.science/pith/46XFAD7AIRY37Q3U5VUQULYLUC/bundle.json","state":"https://pith.science/pith/46XFAD7AIRY37Q3U5VUQULYLUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/46XFAD7AIRY37Q3U5VUQULYLUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:46XFAD7AIRY37Q3U5VUQULYLUC","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":"b52cc305ec75d6729fdcb9cf4291ed20ab0008b8d717a4b27f23832427609b46","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T05:08:52Z","title_canon_sha256":"bd5522dd2cb463f144f707ae489d644b0a5923d4ee0abcdffa07573d5400da3f"},"schema_version":"1.0","source":{"id":"2605.13014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13014","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13014v1","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13014","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"pith_short_12","alias_value":"46XFAD7AIRY3","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"46XFAD7AIRY37Q3U","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"46XFAD7A","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:562dd3a54d541e627fa34e7560e3acf8f8a0126d2f392e3f9568ceb827cc7d78","target":"graph","created_at":"2026-05-18T03:09:00Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We also explicitly construct some spectral triples in which the Connes spectral distances between quantum states are exactly the quantum trace distances."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The assumption that the chosen finite-dimensional matrix algebra representations and spectral triples are sufficient to capture the relevant geometric and distance properties of general quantum states."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Connes spectral distances are unitarily invariant and can be constructed to equal quantum trace distances in certain finite spectral triples."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Connes spectral distances between quantum states remain unchanged under unitary transformations in finite spectral triples."}],"snapshot_sha256":"19e06523161519df9b56e42f2b14a581c6d61c43194b879eac265aa3c71bf45b"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8798b455b0bae44f1e684c18cfb6981c43ee198348776c4a8017e3318cb521b1"},"paper":{"abstract_excerpt":"In this paper, we study the properties of Connes spectral distances between quantum states under unitary transformations. We mainly focus on spectral triples with matrix algebras acting on finite dimensional Hilbert spaces via some linear representations. We derive some elementary properties of the Connes spectral distances and optimal elements. We prove that there are some finite spectral triples in which the Lipschitz seminorms are equal to the operator norms. We also explicitly construct some spectral triples in which the Connes spectral distances between quantum states are exactly the quan","authors_text":"Bing-Sheng Lin, Ji-Hong Wang, Zhi-Kang You","cross_cats":["math.MP"],"headline":"Connes spectral distances between quantum states remain unchanged under unitary transformations in finite spectral triples.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T05:08:52Z","title":"Unitary invariance of Connes spectral distances of quantum states"},"references":{"count":24,"internal_anchors":0,"resolved_work":24,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Connes,Noncommutative geometry(Academic Press, New York, 1994)","work_id":"c6460f40-a7e8-4261-9f5a-57eb16730d75","year":1994},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Compact metric spaces, Fredholm modules and hyperfinite- ness","work_id":"25046f91-8454-44c5-bd0c-2b7ac6793c8c","year":1989},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Distances on a lattice from non- commutative geometry","work_id":"5185bd04-3e82-47dd-ab43-25c6a932aa3e","year":1994},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Connes’ distance of one-dimensional lattices: general cases","work_id":"aa38e3ce-7b6d-4922-9d1c-f4928ee56fa6","year":2001},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"The spectral dis- tance on the Moyal plane","work_id":"16602d11-fccc-4a42-949e-66602e4909d9","year":2011}],"snapshot_sha256":"0b5554615f198a2f6e5060bedaef8d9b918d31afa39aff468661d34211d72390"},"source":{"id":"2605.13014","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T17:28:44.534952Z","id":"bfa40eaf-90a8-4e1e-8df5-b61fce1a0106","model_set":{"reader":"grok-4.3"},"one_line_summary":"Connes spectral distances are unitarily invariant and can be constructed to equal quantum trace distances in certain finite spectral triples.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Connes spectral distances between quantum states remain unchanged under unitary transformations in finite spectral triples.","strongest_claim":"We also explicitly construct some spectral triples in which the Connes spectral distances between quantum states are exactly the quantum trace distances.","weakest_assumption":"The assumption that the chosen finite-dimensional matrix algebra representations and spectral triples are sufficient to capture the relevant geometric and distance properties of general quantum states."}},"verdict_id":"bfa40eaf-90a8-4e1e-8df5-b61fce1a0106"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:41c50c1b96c65f459298a75d0bace0da6f1b797ebe7956a6632dce912fc1c1b1","target":"record","created_at":"2026-05-18T03:09:00Z","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":"b52cc305ec75d6729fdcb9cf4291ed20ab0008b8d717a4b27f23832427609b46","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T05:08:52Z","title_canon_sha256":"bd5522dd2cb463f144f707ae489d644b0a5923d4ee0abcdffa07573d5400da3f"},"schema_version":"1.0","source":{"id":"2605.13014","kind":"arxiv","version":1}},"canonical_sha256":"e7ae500fe04471bfc374ed690a2f0ba09340e70e65e172020fbe138e4b1cd047","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7ae500fe04471bfc374ed690a2f0ba09340e70e65e172020fbe138e4b1cd047","first_computed_at":"2026-05-18T03:09:00.189969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:00.189969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tavDEtlyNNJmq1MgSTToAkLNSP56LjjcedEpiPR+3a+PY6ckmm04TjAvKp1ucXjK95x6Yh62NB8xu/9E7iXgDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:00.190969Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41c50c1b96c65f459298a75d0bace0da6f1b797ebe7956a6632dce912fc1c1b1","sha256:562dd3a54d541e627fa34e7560e3acf8f8a0126d2f392e3f9568ceb827cc7d78"],"state_sha256":"c356d046809e4424bc4f7793e90ed6858deb6582a1998b8e49b3f711e26865b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XJ7gQQyN9dM8yL04KLldoYD7pz8neeCkQNzamVaIcPeTaA+s/cp0tRmb4WUkAkTS3Vv1FuAlgTQIewI8ta0DCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:37:15.128672Z","bundle_sha256":"e770cf2c37eb1d6b5d512a39b4c8a6afb749a2cdd4645cde5770da7c0b52aabd"}}