{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:V4U6DXKOJ34XB264I3EDH5FSH7","short_pith_number":"pith:V4U6DXKO","canonical_record":{"source":{"id":"1309.7514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-29T00:50:59Z","cross_cats_sorted":["math-ph","math.AG","math.CT","math.MP"],"title_canon_sha256":"a9236682082610b4669069b415cbbaae70123876bb1ca4ea1561a06a07a55a2b","abstract_canon_sha256":"5a3d87ecf2085105939dbf025e8dab52e27a82a84790f72a48d36231760e508d"},"schema_version":"1.0"},"canonical_sha256":"af29e1dd4e4ef970ebdc46c833f4b23fca3b1052b473529cb4b7cb2d074c3cc7","source":{"kind":"arxiv","id":"1309.7514","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7514","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7514v1","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7514","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"V4U6DXKOJ34X","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V4U6DXKOJ34XB264","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V4U6DXKO","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:V4U6DXKOJ34XB264I3EDH5FSH7","target":"record","payload":{"canonical_record":{"source":{"id":"1309.7514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-29T00:50:59Z","cross_cats_sorted":["math-ph","math.AG","math.CT","math.MP"],"title_canon_sha256":"a9236682082610b4669069b415cbbaae70123876bb1ca4ea1561a06a07a55a2b","abstract_canon_sha256":"5a3d87ecf2085105939dbf025e8dab52e27a82a84790f72a48d36231760e508d"},"schema_version":"1.0"},"canonical_sha256":"af29e1dd4e4ef970ebdc46c833f4b23fca3b1052b473529cb4b7cb2d074c3cc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:56.756371Z","signature_b64":"gL09ewrZPRGQQWyAy7kIw8oykbOcgGLemzPQiWSoIFWe2pwXvI1bjMByohEARMfC5NDumU1r6iyc85c05shxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af29e1dd4e4ef970ebdc46c833f4b23fca3b1052b473529cb4b7cb2d074c3cc7","last_reissued_at":"2026-05-18T03:11:56.755639Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:56.755639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.7514","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":"2026-05-18T03:11:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eYxlU3TVE5JQkLKDXFvC1itP5xPIO2jPe4v7nGIxfYoR0sbHHH6FvJCGnqGewsD7DTozQy/l6j9zIeiybX+qAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:11:32.130698Z"},"content_sha256":"5d37b0912459b150bc0d5d01107659246bce83cf2c3761d8338bba01f57e8a6a","schema_version":"1.0","event_id":"sha256:5d37b0912459b150bc0d5d01107659246bce83cf2c3761d8338bba01f57e8a6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:V4U6DXKOJ34XB264I3EDH5FSH7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinity Links L, infinity-4-Manifolds M_L and Kirby Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.CT","math.MP"],"primary_cat":"math.GT","authors_text":"Renaud Gauthier","submitted_at":"2013-09-29T00:50:59Z","abstract_excerpt":"We construct what we call a Kirby category, a monoidal category whose morphisms are smooth 4-manifolds, projecting down to another monoidal category whose morphisms are orientable 3-manifolds, the projection being induced by the boundary map on manifolds. We construct a higher categorical generalization of such concepts and introduce the notion of ribbon $\\infty$-categories, a generalization of braided monoidal $\\infty$-categories (\\cite{Lu1}), which gives rise to the concepts of $\\infty$-links, $\\infty$-4-manifolds as well as the more general notion of walled $\\infty$-4-manifolds if one focus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7514","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":"2026-05-18T03:11:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iea8C7eDQJxiiqkQxPZW8gd2/xGnaQmuPltrDmRQOuXFAWu7CBq0fwPYMOXCpqqY7qJKgqE1Ep+mOR5Dy2lhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:11:32.131050Z"},"content_sha256":"d85ad47ca2ba5136d6dd9d79789273bbc2b8c3ea2127ea51b33cae490419e078","schema_version":"1.0","event_id":"sha256:d85ad47ca2ba5136d6dd9d79789273bbc2b8c3ea2127ea51b33cae490419e078"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4U6DXKOJ34XB264I3EDH5FSH7/bundle.json","state_url":"https://pith.science/pith/V4U6DXKOJ34XB264I3EDH5FSH7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4U6DXKOJ34XB264I3EDH5FSH7/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":"2026-06-12T07:11:32Z","links":{"resolver":"https://pith.science/pith/V4U6DXKOJ34XB264I3EDH5FSH7","bundle":"https://pith.science/pith/V4U6DXKOJ34XB264I3EDH5FSH7/bundle.json","state":"https://pith.science/pith/V4U6DXKOJ34XB264I3EDH5FSH7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4U6DXKOJ34XB264I3EDH5FSH7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V4U6DXKOJ34XB264I3EDH5FSH7","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":"5a3d87ecf2085105939dbf025e8dab52e27a82a84790f72a48d36231760e508d","cross_cats_sorted":["math-ph","math.AG","math.CT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-29T00:50:59Z","title_canon_sha256":"a9236682082610b4669069b415cbbaae70123876bb1ca4ea1561a06a07a55a2b"},"schema_version":"1.0","source":{"id":"1309.7514","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7514","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7514v1","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7514","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"V4U6DXKOJ34X","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V4U6DXKOJ34XB264","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V4U6DXKO","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:d85ad47ca2ba5136d6dd9d79789273bbc2b8c3ea2127ea51b33cae490419e078","target":"graph","created_at":"2026-05-18T03:11:56Z","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":"We construct what we call a Kirby category, a monoidal category whose morphisms are smooth 4-manifolds, projecting down to another monoidal category whose morphisms are orientable 3-manifolds, the projection being induced by the boundary map on manifolds. We construct a higher categorical generalization of such concepts and introduce the notion of ribbon $\\infty$-categories, a generalization of braided monoidal $\\infty$-categories (\\cite{Lu1}), which gives rise to the concepts of $\\infty$-links, $\\infty$-4-manifolds as well as the more general notion of walled $\\infty$-4-manifolds if one focus","authors_text":"Renaud Gauthier","cross_cats":["math-ph","math.AG","math.CT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-29T00:50:59Z","title":"Infinity Links L, infinity-4-Manifolds M_L and Kirby Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7514","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":"sha256:5d37b0912459b150bc0d5d01107659246bce83cf2c3761d8338bba01f57e8a6a","target":"record","created_at":"2026-05-18T03:11:56Z","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":"5a3d87ecf2085105939dbf025e8dab52e27a82a84790f72a48d36231760e508d","cross_cats_sorted":["math-ph","math.AG","math.CT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-29T00:50:59Z","title_canon_sha256":"a9236682082610b4669069b415cbbaae70123876bb1ca4ea1561a06a07a55a2b"},"schema_version":"1.0","source":{"id":"1309.7514","kind":"arxiv","version":1}},"canonical_sha256":"af29e1dd4e4ef970ebdc46c833f4b23fca3b1052b473529cb4b7cb2d074c3cc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af29e1dd4e4ef970ebdc46c833f4b23fca3b1052b473529cb4b7cb2d074c3cc7","first_computed_at":"2026-05-18T03:11:56.755639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:56.755639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gL09ewrZPRGQQWyAy7kIw8oykbOcgGLemzPQiWSoIFWe2pwXvI1bjMByohEARMfC5NDumU1r6iyc85c05shxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:56.756371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7514","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d37b0912459b150bc0d5d01107659246bce83cf2c3761d8338bba01f57e8a6a","sha256:d85ad47ca2ba5136d6dd9d79789273bbc2b8c3ea2127ea51b33cae490419e078"],"state_sha256":"37a4cc64ef38525c48fb74b90ef8fd4cefc246de99ce8846af136df7502f2efb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xbPsAbg+998I4vCLXFwBWkUPAk/Xk/sQQKlVpvWcOor/qILXOqcGhOk7zm1ji9XzI/DHQHp8+EmdGiAig9xPDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T07:11:32.133003Z","bundle_sha256":"2d5be48349dd1e60ce4530961eaf7ea6aad113795ad51d5c954cc253a72a2b5c"}}