{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:47DSEPS26XU4RRU3ELDABST4Y6","short_pith_number":"pith:47DSEPS2","canonical_record":{"source":{"id":"math-ph/0104002","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-04-01T17:37:03Z","cross_cats_sorted":["hep-lat","hep-th","math.MP","math.QA"],"title_canon_sha256":"6bdd8c3a2fb759c386dcdbdb6c06896693d204a021b343606c2148041f645104","abstract_canon_sha256":"a0ba300bf6fdddb32d7f799b150207c9e02af89010dc58a658fa0b2d2ddd9d46"},"schema_version":"1.0"},"canonical_sha256":"e7c7223e5af5e9c8c69b22c600ca7cc7b28fc38d961a377ef0bc116093406fcb","source":{"kind":"arxiv","id":"math-ph/0104002","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0104002","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0104002v1","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0104002","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"47DSEPS26XU4","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"47DSEPS26XU4RRU3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"47DSEPS2","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:47DSEPS26XU4RRU3ELDABST4Y6","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0104002","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-04-01T17:37:03Z","cross_cats_sorted":["hep-lat","hep-th","math.MP","math.QA"],"title_canon_sha256":"6bdd8c3a2fb759c386dcdbdb6c06896693d204a021b343606c2148041f645104","abstract_canon_sha256":"a0ba300bf6fdddb32d7f799b150207c9e02af89010dc58a658fa0b2d2ddd9d46"},"schema_version":"1.0"},"canonical_sha256":"e7c7223e5af5e9c8c69b22c600ca7cc7b28fc38d961a377ef0bc116093406fcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:46.086283Z","signature_b64":"guHXhnlUgpIg0TluNwRkYLJPsRABj3dWDA0Iuxilv6IO1uEqDOlOkhxqe/lz2lBrIAqxVgfZHzOOHVoXZKnhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7c7223e5af5e9c8c69b22c600ca7cc7b28fc38d961a377ef0bc116093406fcb","last_reissued_at":"2026-05-18T00:25:46.085838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:46.085838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0104002","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":"2026-05-18T00:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HamFGDX0mCW9jH3F+o8wZxM1lgVs9LNGICX/BkSWqFbPOw3ixrzlip5ZzBWefgOs26BSQcHPRChGrhG4vBonBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:07:43.506128Z"},"content_sha256":"f9f96006c192f1586fded4883bc95e5b8519d57b79807b602a14cca45463f303","schema_version":"1.0","event_id":"sha256:f9f96006c192f1586fded4883bc95e5b8519d57b79807b602a14cca45463f303"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:47DSEPS26XU4RRU3ELDABST4Y6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connes' Distance of One-Dimensional Lattices: General Cases","license":"","headline":"","cross_cats":["hep-lat","hep-th","math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Jian Dai, Xing-Chang Song","submitted_at":"2001-04-01T17:37:03Z","abstract_excerpt":"Connes' distance formula is applied to endow linear metric to three 1D lattices of different topology, with a generalization of lattice Dirac operator written down by Dimakis et al to contain a non-unitary link-variable. Geometric interpretation of this link-variable is lattice spacing and parallel transport."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0104002","kind":"arxiv","version":1},"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":"2026-05-18T00:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pLc/9r0IxwOKf0Y9OfKzp3DSgRROHr5MsjGtS8j3OeOdtSs229zcXacETwy3fcfEsj3nzAJMtCTr/w63C5TQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:07:43.506512Z"},"content_sha256":"8d8d2cb219fff6211aff6df3db6e4b5429589c8945075eb7688a3d8c088f5532","schema_version":"1.0","event_id":"sha256:8d8d2cb219fff6211aff6df3db6e4b5429589c8945075eb7688a3d8c088f5532"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/47DSEPS26XU4RRU3ELDABST4Y6/bundle.json","state_url":"https://pith.science/pith/47DSEPS26XU4RRU3ELDABST4Y6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/47DSEPS26XU4RRU3ELDABST4Y6/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":"2026-06-03T13:07:43Z","links":{"resolver":"https://pith.science/pith/47DSEPS26XU4RRU3ELDABST4Y6","bundle":"https://pith.science/pith/47DSEPS26XU4RRU3ELDABST4Y6/bundle.json","state":"https://pith.science/pith/47DSEPS26XU4RRU3ELDABST4Y6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/47DSEPS26XU4RRU3ELDABST4Y6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:47DSEPS26XU4RRU3ELDABST4Y6","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":"a0ba300bf6fdddb32d7f799b150207c9e02af89010dc58a658fa0b2d2ddd9d46","cross_cats_sorted":["hep-lat","hep-th","math.MP","math.QA"],"license":"","primary_cat":"math-ph","submitted_at":"2001-04-01T17:37:03Z","title_canon_sha256":"6bdd8c3a2fb759c386dcdbdb6c06896693d204a021b343606c2148041f645104"},"schema_version":"1.0","source":{"id":"math-ph/0104002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0104002","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0104002v1","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0104002","created_at":"2026-05-18T00:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"47DSEPS26XU4","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"47DSEPS26XU4RRU3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"47DSEPS2","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:8d8d2cb219fff6211aff6df3db6e4b5429589c8945075eb7688a3d8c088f5532","target":"graph","created_at":"2026-05-18T00:25:46Z","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":"Connes' distance formula is applied to endow linear metric to three 1D lattices of different topology, with a generalization of lattice Dirac operator written down by Dimakis et al to contain a non-unitary link-variable. Geometric interpretation of this link-variable is lattice spacing and parallel transport.","authors_text":"Jian Dai, Xing-Chang Song","cross_cats":["hep-lat","hep-th","math.MP","math.QA"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2001-04-01T17:37:03Z","title":"Connes' Distance of One-Dimensional Lattices: General Cases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0104002","kind":"arxiv","version":1},"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:f9f96006c192f1586fded4883bc95e5b8519d57b79807b602a14cca45463f303","target":"record","created_at":"2026-05-18T00:25:46Z","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":"a0ba300bf6fdddb32d7f799b150207c9e02af89010dc58a658fa0b2d2ddd9d46","cross_cats_sorted":["hep-lat","hep-th","math.MP","math.QA"],"license":"","primary_cat":"math-ph","submitted_at":"2001-04-01T17:37:03Z","title_canon_sha256":"6bdd8c3a2fb759c386dcdbdb6c06896693d204a021b343606c2148041f645104"},"schema_version":"1.0","source":{"id":"math-ph/0104002","kind":"arxiv","version":1}},"canonical_sha256":"e7c7223e5af5e9c8c69b22c600ca7cc7b28fc38d961a377ef0bc116093406fcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7c7223e5af5e9c8c69b22c600ca7cc7b28fc38d961a377ef0bc116093406fcb","first_computed_at":"2026-05-18T00:25:46.085838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:46.085838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"guHXhnlUgpIg0TluNwRkYLJPsRABj3dWDA0Iuxilv6IO1uEqDOlOkhxqe/lz2lBrIAqxVgfZHzOOHVoXZKnhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:46.086283Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0104002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9f96006c192f1586fded4883bc95e5b8519d57b79807b602a14cca45463f303","sha256:8d8d2cb219fff6211aff6df3db6e4b5429589c8945075eb7688a3d8c088f5532"],"state_sha256":"1ed35667695d694a7c1dd9fd12c3f2b9fc264fb544eaa49b3f2abfbdb40e4965"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ISo7tRn9Irg9VlRp+1OuH1IfUttj5zQUFMl1EF/RUtmTsQ7ofIAN0YqZ62Pl5pukRTQTJt64IkeyCAbWRAvQCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T13:07:43.508592Z","bundle_sha256":"5e5472f00120fb6dd7fd2256cf54b3560bd49afc68ac9192d9c6a0fc48effa32"}}