{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XLZNTPABGLMYNXEHWNN7QR2MXT","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":"3f08280d334540b6a9a066996fd9ba3ff26e893d8e9386caefb44cb67ef060ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-06-20T12:05:13Z","title_canon_sha256":"49bce2b3d22275d0a00873c316040a0e414edd6a364e5a2103a7201feb2d3b1a"},"schema_version":"1.0","source":{"id":"1306.4841","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4841","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4841v3","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4841","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"XLZNTPABGLMY","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XLZNTPABGLMYNXEH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XLZNTPAB","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:e102e57d0523a2594f4703bc0a0ece6e6eb3d6871818253b0c80c99f0fd5a2b2","target":"graph","created_at":"2026-05-18T00:18:56Z","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":"This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in computations. The novelty of the approach is we rely heavily on the naturality of binary symmetric groups to avoid lengthy explicit constructions of smoothings of PL-manifolds.","authors_text":"Ryan Budney","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-06-20T12:05:13Z","title":"Combinatorial spin structures on triangulated manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4841","kind":"arxiv","version":3},"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:fbc46582e457b32cb8b4eabc4fe0e9d1c0029ba0c2f47628b27e98e5a71b72af","target":"record","created_at":"2026-05-18T00:18:56Z","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":"3f08280d334540b6a9a066996fd9ba3ff26e893d8e9386caefb44cb67ef060ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-06-20T12:05:13Z","title_canon_sha256":"49bce2b3d22275d0a00873c316040a0e414edd6a364e5a2103a7201feb2d3b1a"},"schema_version":"1.0","source":{"id":"1306.4841","kind":"arxiv","version":3}},"canonical_sha256":"baf2d9bc0132d986dc87b35bf8474cbcd1c6a4d0c333c61f29d6ba8f49d63a89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baf2d9bc0132d986dc87b35bf8474cbcd1c6a4d0c333c61f29d6ba8f49d63a89","first_computed_at":"2026-05-18T00:18:56.268964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:56.268964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vv7Oeq2JQg+TYW2doMkhyTzJuvwb+mjJ9qqMXMkRHKxxxpSyMnjMHqkjwRDxaqIB2fQTEfCqSliF1R/xw4r/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:56.269461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4841","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbc46582e457b32cb8b4eabc4fe0e9d1c0029ba0c2f47628b27e98e5a71b72af","sha256:e102e57d0523a2594f4703bc0a0ece6e6eb3d6871818253b0c80c99f0fd5a2b2"],"state_sha256":"54dd6e4f094b06dbf121a75a28aff8c3c21e2b67c71cc6f8e6d643d70cf05316"}