{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZGHXSJKV2NS45C5TRBL42VUBTV","short_pith_number":"pith:ZGHXSJKV","canonical_record":{"source":{"id":"1206.5164","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-22T14:37:09Z","cross_cats_sorted":[],"title_canon_sha256":"da73dd73faeb19e5a3c4c79a9f1c2556d859aead957ea4264c51add22a29e100","abstract_canon_sha256":"1a6a1a93b8ae649c535812baffd7dc308c698d41de93359a5afd37e55a0b5571"},"schema_version":"1.0"},"canonical_sha256":"c98f792555d365ce8bb38857cd56819d5121b1d09454faad5e5a3ba96de98386","source":{"kind":"arxiv","id":"1206.5164","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5164","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5164v3","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5164","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZGHXSJKV2NS4","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZGHXSJKV2NS45C5T","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZGHXSJKV","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZGHXSJKV2NS45C5TRBL42VUBTV","target":"record","payload":{"canonical_record":{"source":{"id":"1206.5164","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-22T14:37:09Z","cross_cats_sorted":[],"title_canon_sha256":"da73dd73faeb19e5a3c4c79a9f1c2556d859aead957ea4264c51add22a29e100","abstract_canon_sha256":"1a6a1a93b8ae649c535812baffd7dc308c698d41de93359a5afd37e55a0b5571"},"schema_version":"1.0"},"canonical_sha256":"c98f792555d365ce8bb38857cd56819d5121b1d09454faad5e5a3ba96de98386","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:58.478395Z","signature_b64":"7Cmzyo5Gazozp6M4syNHrt/vk3NwqlkKmcq1LSTYV7MCb8JIId2Jx93WYgXt+YxF2ImDypxwkuhzqMjiA18hCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c98f792555d365ce8bb38857cd56819d5121b1d09454faad5e5a3ba96de98386","last_reissued_at":"2026-05-18T02:41:58.477963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:58.477963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.5164","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zCIg6ljqmyrcAkzxt5buUydEy//VkNRSRAP59dasGPrPHklaoOtaEA33j/EVWjzVXuUuhIu6V+7Qjw9EH/seCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:55:14.811528Z"},"content_sha256":"0c95307a270537efce09ad9f81d79efed1955b9b75a09b973625453be01f5ba7","schema_version":"1.0","event_id":"sha256:0c95307a270537efce09ad9f81d79efed1955b9b75a09b973625453be01f5ba7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZGHXSJKV2NS45C5TRBL42VUBTV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structured singular manifolds and factorization homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"David Ayala, Hiro Lee Tanaka, John Francis","submitted_at":"2012-06-22T14:37:09Z","abstract_excerpt":"We provide a framework for the study of structured manifolds with singularities and their locally determined invariants. This generalizes factorization homology, or topological chiral homology, to the setting of singular manifolds equipped with various tangential structures. Examples of such factorization homology theories include intersection homology, compactly supported stratified mapping spaces, and Hochschild homology with coefficients. Factorization homology theories for singular manifolds are characterized by a generalization of the Eilenberg-Steenrod axioms. Using these axioms, we exte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5164","kind":"arxiv","version":3},"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":"2026-05-18T02:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VheS1ujXd3X4xDTTOokOvbPlBTxuTlYPJ0Tmo7AfBU/0OANueFbMZ82b1bO0mBYvJHDWcUi4JEirKif6C1p6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:55:14.811874Z"},"content_sha256":"3a490871e5bc06a8f0b2445798058bd141892dc71810127bb6d86749ecfea521","schema_version":"1.0","event_id":"sha256:3a490871e5bc06a8f0b2445798058bd141892dc71810127bb6d86749ecfea521"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZGHXSJKV2NS45C5TRBL42VUBTV/bundle.json","state_url":"https://pith.science/pith/ZGHXSJKV2NS45C5TRBL42VUBTV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZGHXSJKV2NS45C5TRBL42VUBTV/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":"2026-06-02T18:55:14Z","links":{"resolver":"https://pith.science/pith/ZGHXSJKV2NS45C5TRBL42VUBTV","bundle":"https://pith.science/pith/ZGHXSJKV2NS45C5TRBL42VUBTV/bundle.json","state":"https://pith.science/pith/ZGHXSJKV2NS45C5TRBL42VUBTV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZGHXSJKV2NS45C5TRBL42VUBTV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZGHXSJKV2NS45C5TRBL42VUBTV","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":"1a6a1a93b8ae649c535812baffd7dc308c698d41de93359a5afd37e55a0b5571","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-22T14:37:09Z","title_canon_sha256":"da73dd73faeb19e5a3c4c79a9f1c2556d859aead957ea4264c51add22a29e100"},"schema_version":"1.0","source":{"id":"1206.5164","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5164","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5164v3","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5164","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZGHXSJKV2NS4","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZGHXSJKV2NS45C5T","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZGHXSJKV","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:3a490871e5bc06a8f0b2445798058bd141892dc71810127bb6d86749ecfea521","target":"graph","created_at":"2026-05-18T02:41:58Z","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 provide a framework for the study of structured manifolds with singularities and their locally determined invariants. This generalizes factorization homology, or topological chiral homology, to the setting of singular manifolds equipped with various tangential structures. Examples of such factorization homology theories include intersection homology, compactly supported stratified mapping spaces, and Hochschild homology with coefficients. Factorization homology theories for singular manifolds are characterized by a generalization of the Eilenberg-Steenrod axioms. Using these axioms, we exte","authors_text":"David Ayala, Hiro Lee Tanaka, John Francis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-22T14:37:09Z","title":"Structured singular manifolds and factorization homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5164","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":"sha256:0c95307a270537efce09ad9f81d79efed1955b9b75a09b973625453be01f5ba7","target":"record","created_at":"2026-05-18T02:41:58Z","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":"1a6a1a93b8ae649c535812baffd7dc308c698d41de93359a5afd37e55a0b5571","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-22T14:37:09Z","title_canon_sha256":"da73dd73faeb19e5a3c4c79a9f1c2556d859aead957ea4264c51add22a29e100"},"schema_version":"1.0","source":{"id":"1206.5164","kind":"arxiv","version":3}},"canonical_sha256":"c98f792555d365ce8bb38857cd56819d5121b1d09454faad5e5a3ba96de98386","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c98f792555d365ce8bb38857cd56819d5121b1d09454faad5e5a3ba96de98386","first_computed_at":"2026-05-18T02:41:58.477963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:58.477963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Cmzyo5Gazozp6M4syNHrt/vk3NwqlkKmcq1LSTYV7MCb8JIId2Jx93WYgXt+YxF2ImDypxwkuhzqMjiA18hCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:58.478395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5164","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c95307a270537efce09ad9f81d79efed1955b9b75a09b973625453be01f5ba7","sha256:3a490871e5bc06a8f0b2445798058bd141892dc71810127bb6d86749ecfea521"],"state_sha256":"fb735c41972e7f2f79e0cb6486872d16101d8251f9fd8459245d3af53d9411f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0wyHqI0a/ezYncxE8qImfCYRV5Lrnyo/lrKnZiPO8KFKs1mZWt06GPLtGpnxL2W88OFgJVnSZPfFMLwCAlj6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:55:14.813839Z","bundle_sha256":"8e1c54af0ffc1057d96fab99e5cc959ea4ba76f5a0f136c7539834a8245231ca"}}