{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Y5V5VJP32OGRR7BCUEQQKMDQJU","short_pith_number":"pith:Y5V5VJP3","canonical_record":{"source":{"id":"1811.01119","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-11-02T23:05:17Z","cross_cats_sorted":[],"title_canon_sha256":"4451a2f3d3c746fd39012e2bb7614e5b06edd9668d53667bc294486a183149c6","abstract_canon_sha256":"281a935ffc8eca95b407f5571635bde5bfa907410e62404e47155329009bc9a5"},"schema_version":"1.0"},"canonical_sha256":"c76bdaa5fbd38d18fc22a1210530704d1e66b6f88e088bbc7e0b90a460e181ed","source":{"kind":"arxiv","id":"1811.01119","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01119","created_at":"2026-07-05T05:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01119v6","created_at":"2026-07-05T05:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01119","created_at":"2026-07-05T05:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"Y5V5VJP32OGR","created_at":"2026-07-05T05:54:09Z"},{"alias_kind":"pith_short_16","alias_value":"Y5V5VJP32OGRR7BC","created_at":"2026-07-05T05:54:09Z"},{"alias_kind":"pith_short_8","alias_value":"Y5V5VJP3","created_at":"2026-07-05T05:54:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Y5V5VJP32OGRR7BCUEQQKMDQJU","target":"record","payload":{"canonical_record":{"source":{"id":"1811.01119","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-11-02T23:05:17Z","cross_cats_sorted":[],"title_canon_sha256":"4451a2f3d3c746fd39012e2bb7614e5b06edd9668d53667bc294486a183149c6","abstract_canon_sha256":"281a935ffc8eca95b407f5571635bde5bfa907410e62404e47155329009bc9a5"},"schema_version":"1.0"},"canonical_sha256":"c76bdaa5fbd38d18fc22a1210530704d1e66b6f88e088bbc7e0b90a460e181ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:54:09.782075Z","signature_b64":"VeXX2sb7WO7oTnT9IscnTAyTTfa4lcnUdKqVyCEmHLK1ea64m1SUBFspPMDCPS5SgnXMvN9WqpsxWv5AI5jtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c76bdaa5fbd38d18fc22a1210530704d1e66b6f88e088bbc7e0b90a460e181ed","last_reissued_at":"2026-07-05T05:54:09.781604Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:54:09.781604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.01119","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:54:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TWhXzHsV1U1qrIAETF/h83a1UID74jv9qQNEk0dp4vVj2i3QUHc7VNcZV+9A6YQdE/YfQU01dn0bvIUZilwBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:29:49.273904Z"},"content_sha256":"74945b33b63a13f4a1e10896d61cb143e01f1b11341390b160e2149e8d5759b3","schema_version":"1.0","event_id":"sha256:74945b33b63a13f4a1e10896d61cb143e01f1b11341390b160e2149e8d5759b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Y5V5VJP32OGRR7BCUEQQKMDQJU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the homotopy theory of stratified spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Peter J. Haine","submitted_at":"2018-11-02T23:05:17Z","abstract_excerpt":"Let $P$ be a poset. We define a new homotopy theory of suitably nice $P$-stratified topological spaces with equivalences on strata and links inverted. We show that the exit-path construction of MacPherson, Treumann, and Lurie defines an equivalence from our homotopy theory of $P$-stratified topological spaces to the $\\infty$-category of $\\infty$-categories with a conservative functor to $P$. This proves a stratified form of Grothendieck's homotopy hypothesis, verifying a conjecture of Ayala-Francis-Rozenblyum. Our homotopy theory of stratified spaces has the added benefit of capturing all exam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01119","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1811.01119/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:54:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"anLkpD4jCYNn8ltiouBaRGKFKfiEL/8qaosDZk1finUvQ6yuQyb3kL2rdJr2WnagC6dMmfjhg6QlMRRijDT6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:29:49.274442Z"},"content_sha256":"ce85433aa85cbd142179bce3dfa8a83dcfaff7d5b17bc0479427653e7395972d","schema_version":"1.0","event_id":"sha256:ce85433aa85cbd142179bce3dfa8a83dcfaff7d5b17bc0479427653e7395972d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5V5VJP32OGRR7BCUEQQKMDQJU/bundle.json","state_url":"https://pith.science/pith/Y5V5VJP32OGRR7BCUEQQKMDQJU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5V5VJP32OGRR7BCUEQQKMDQJU/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":"2026-08-16T19:29:49Z","links":{"resolver":"https://pith.science/pith/Y5V5VJP32OGRR7BCUEQQKMDQJU","bundle":"https://pith.science/pith/Y5V5VJP32OGRR7BCUEQQKMDQJU/bundle.json","state":"https://pith.science/pith/Y5V5VJP32OGRR7BCUEQQKMDQJU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5V5VJP32OGRR7BCUEQQKMDQJU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Y5V5VJP32OGRR7BCUEQQKMDQJU","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":"281a935ffc8eca95b407f5571635bde5bfa907410e62404e47155329009bc9a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-11-02T23:05:17Z","title_canon_sha256":"4451a2f3d3c746fd39012e2bb7614e5b06edd9668d53667bc294486a183149c6"},"schema_version":"1.0","source":{"id":"1811.01119","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01119","created_at":"2026-07-05T05:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01119v6","created_at":"2026-07-05T05:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01119","created_at":"2026-07-05T05:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"Y5V5VJP32OGR","created_at":"2026-07-05T05:54:09Z"},{"alias_kind":"pith_short_16","alias_value":"Y5V5VJP32OGRR7BC","created_at":"2026-07-05T05:54:09Z"},{"alias_kind":"pith_short_8","alias_value":"Y5V5VJP3","created_at":"2026-07-05T05:54:09Z"}],"graph_snapshots":[{"event_id":"sha256:ce85433aa85cbd142179bce3dfa8a83dcfaff7d5b17bc0479427653e7395972d","target":"graph","created_at":"2026-07-05T05:54:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1811.01119/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $P$ be a poset. We define a new homotopy theory of suitably nice $P$-stratified topological spaces with equivalences on strata and links inverted. We show that the exit-path construction of MacPherson, Treumann, and Lurie defines an equivalence from our homotopy theory of $P$-stratified topological spaces to the $\\infty$-category of $\\infty$-categories with a conservative functor to $P$. This proves a stratified form of Grothendieck's homotopy hypothesis, verifying a conjecture of Ayala-Francis-Rozenblyum. Our homotopy theory of stratified spaces has the added benefit of capturing all exam","authors_text":"Peter J. Haine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-11-02T23:05:17Z","title":"On the homotopy theory of stratified spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01119","kind":"arxiv","version":6},"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":"sha256:74945b33b63a13f4a1e10896d61cb143e01f1b11341390b160e2149e8d5759b3","target":"record","created_at":"2026-07-05T05:54:09Z","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":"281a935ffc8eca95b407f5571635bde5bfa907410e62404e47155329009bc9a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-11-02T23:05:17Z","title_canon_sha256":"4451a2f3d3c746fd39012e2bb7614e5b06edd9668d53667bc294486a183149c6"},"schema_version":"1.0","source":{"id":"1811.01119","kind":"arxiv","version":6}},"canonical_sha256":"c76bdaa5fbd38d18fc22a1210530704d1e66b6f88e088bbc7e0b90a460e181ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c76bdaa5fbd38d18fc22a1210530704d1e66b6f88e088bbc7e0b90a460e181ed","first_computed_at":"2026-07-05T05:54:09.781604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:54:09.781604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VeXX2sb7WO7oTnT9IscnTAyTTfa4lcnUdKqVyCEmHLK1ea64m1SUBFspPMDCPS5SgnXMvN9WqpsxWv5AI5jtAg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:54:09.782075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01119","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74945b33b63a13f4a1e10896d61cb143e01f1b11341390b160e2149e8d5759b3","sha256:ce85433aa85cbd142179bce3dfa8a83dcfaff7d5b17bc0479427653e7395972d"],"state_sha256":"f788f580df92f19d2091d6bc73294994566eeef421f809787599c190452bb8e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dQzyLsg9QymU7ECt5sK6ADxfk4vw2gaeWaMLXAbL9g17iauEKrnN8JvamY0mngmwabaDgx+kX/AAG5eruf7ZBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T19:29:49.278093Z","bundle_sha256":"dbf083dcd896dfdd872ff37f8ee86f7ea5c3fe13830c9dabb76fdd84c35de4cc"}}