{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:MN7TLVY5UNE7NGTVYP3GDOOS4J","short_pith_number":"pith:MN7TLVY5","canonical_record":{"source":{"id":"math/9911256","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"1999-11-20T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"f684119a4bd5b7672cb03afb0884a26400a5bbc85980f53b9c7a6ab5fb386c32","abstract_canon_sha256":"2f8299c7464181a90026f00e384b15eb942d5871a0a9c56c8f6ae883960c97c0"},"schema_version":"1.0"},"canonical_sha256":"637f35d71da349f69a75c3f661b9d2e24a729c9381dd74f1db0337c91ad054ac","source":{"kind":"arxiv","id":"math/9911256","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9911256","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/9911256v1","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9911256","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"MN7TLVY5UNE7","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"MN7TLVY5UNE7NGTV","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"MN7TLVY5","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:MN7TLVY5UNE7NGTVYP3GDOOS4J","target":"record","payload":{"canonical_record":{"source":{"id":"math/9911256","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"1999-11-20T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"f684119a4bd5b7672cb03afb0884a26400a5bbc85980f53b9c7a6ab5fb386c32","abstract_canon_sha256":"2f8299c7464181a90026f00e384b15eb942d5871a0a9c56c8f6ae883960c97c0"},"schema_version":"1.0"},"canonical_sha256":"637f35d71da349f69a75c3f661b9d2e24a729c9381dd74f1db0337c91ad054ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:32.410249Z","signature_b64":"tlYkNEsDaOhgmp1HXX99I/nYeufBiiOOxzm8R7etVoCLNReQJjk/JjUfKTOkBHmNi9i4D4HTaSNZeXr83mMZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"637f35d71da349f69a75c3f661b9d2e24a729c9381dd74f1db0337c91ad054ac","last_reissued_at":"2026-05-18T01:05:32.409666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:32.409666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9911256","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":"2026-05-18T01:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Poj95IgDdvCXZyN/cwXBi/beJc90jkRYG6Zbnfixyl1I2vZc+Mvte5UZnCUDG1duS8F7tN8afHWmOJwxbBLTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T08:28:31.689858Z"},"content_sha256":"073ab5caf8fe9e2fbf83e3c488bdb7f4f0061c18a62a8717386993caebbd12c4","schema_version":"1.0","event_id":"sha256:073ab5caf8fe9e2fbf83e3c488bdb7f4f0061c18a62a8717386993caebbd12c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:MN7TLVY5UNE7NGTVYP3GDOOS4J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simplicial moves on complexes and manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"W. B. R. Lickorish","submitted_at":"1999-11-20T00:00:00Z","abstract_excerpt":"Here are versions of the proofs of two classic theorems of combinatorial topology. The first is the result that piecewise linearly homeomorphic simplicial complexes are related by stellar moves. This is used in the proof, modelled on that of Pachner, of the second theorem. This states that moves from only a finite collection are needed to relate two triangulations of a piecewise linear manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9911256","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":"2026-05-18T01:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KtXmPeXRSxy9WN30TVPKvB1wpbJ02PwPF3ue/M4jHlLJhfCHYT2dury8aYwPV8HL4PHCA01jreJPs4mLwKFoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T08:28:31.690212Z"},"content_sha256":"24b0d53507336cd938f79e7745510414ab61cccd16f7d3c69c656fef3f3b1303","schema_version":"1.0","event_id":"sha256:24b0d53507336cd938f79e7745510414ab61cccd16f7d3c69c656fef3f3b1303"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MN7TLVY5UNE7NGTVYP3GDOOS4J/bundle.json","state_url":"https://pith.science/pith/MN7TLVY5UNE7NGTVYP3GDOOS4J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MN7TLVY5UNE7NGTVYP3GDOOS4J/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":"2026-08-02T08:28:31Z","links":{"resolver":"https://pith.science/pith/MN7TLVY5UNE7NGTVYP3GDOOS4J","bundle":"https://pith.science/pith/MN7TLVY5UNE7NGTVYP3GDOOS4J/bundle.json","state":"https://pith.science/pith/MN7TLVY5UNE7NGTVYP3GDOOS4J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MN7TLVY5UNE7NGTVYP3GDOOS4J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:MN7TLVY5UNE7NGTVYP3GDOOS4J","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":"2f8299c7464181a90026f00e384b15eb942d5871a0a9c56c8f6ae883960c97c0","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"1999-11-20T00:00:00Z","title_canon_sha256":"f684119a4bd5b7672cb03afb0884a26400a5bbc85980f53b9c7a6ab5fb386c32"},"schema_version":"1.0","source":{"id":"math/9911256","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9911256","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/9911256v1","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9911256","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"MN7TLVY5UNE7","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"MN7TLVY5UNE7NGTV","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"MN7TLVY5","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:24b0d53507336cd938f79e7745510414ab61cccd16f7d3c69c656fef3f3b1303","target":"graph","created_at":"2026-05-18T01:05:32Z","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":"Here are versions of the proofs of two classic theorems of combinatorial topology. The first is the result that piecewise linearly homeomorphic simplicial complexes are related by stellar moves. This is used in the proof, modelled on that of Pachner, of the second theorem. This states that moves from only a finite collection are needed to relate two triangulations of a piecewise linear manifold.","authors_text":"W. B. R. Lickorish","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"1999-11-20T00:00:00Z","title":"Simplicial moves on complexes and manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9911256","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":"sha256:073ab5caf8fe9e2fbf83e3c488bdb7f4f0061c18a62a8717386993caebbd12c4","target":"record","created_at":"2026-05-18T01:05:32Z","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":"2f8299c7464181a90026f00e384b15eb942d5871a0a9c56c8f6ae883960c97c0","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"1999-11-20T00:00:00Z","title_canon_sha256":"f684119a4bd5b7672cb03afb0884a26400a5bbc85980f53b9c7a6ab5fb386c32"},"schema_version":"1.0","source":{"id":"math/9911256","kind":"arxiv","version":1}},"canonical_sha256":"637f35d71da349f69a75c3f661b9d2e24a729c9381dd74f1db0337c91ad054ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"637f35d71da349f69a75c3f661b9d2e24a729c9381dd74f1db0337c91ad054ac","first_computed_at":"2026-05-18T01:05:32.409666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:32.409666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tlYkNEsDaOhgmp1HXX99I/nYeufBiiOOxzm8R7etVoCLNReQJjk/JjUfKTOkBHmNi9i4D4HTaSNZeXr83mMZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:32.410249Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9911256","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:073ab5caf8fe9e2fbf83e3c488bdb7f4f0061c18a62a8717386993caebbd12c4","sha256:24b0d53507336cd938f79e7745510414ab61cccd16f7d3c69c656fef3f3b1303"],"state_sha256":"8f20266c2c97f46fe749e936ab143c271ab7925137beeab6bfbe0cd1b7593ae1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rCEbEjTdBsqFP0NMrki1vLl4KoE00ko0XC3o6SZYT748iVjDUHeOmI0DgaItsqisoxFejV1tmYikUMRKBJhBAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T08:28:31.692739Z","bundle_sha256":"9b21427fc00f642e7ee623f83634dd68e0476bd75a6c07c92ba579ed07471385"}}