{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:6HR6WJMTQGNKAGJTSMIVYW5LT5","short_pith_number":"pith:6HR6WJMT","canonical_record":{"source":{"id":"2001.05432","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-01-15T16:59:36Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"dbb9c1064a0e07f846bd64cd3c6e645a86cec078d2914f2d94a14196236251ce","abstract_canon_sha256":"0c088c5b4f074c06e528f730ad0891f2c2f47e744b7da30d64cb9c672d4acd4a"},"schema_version":"1.0"},"canonical_sha256":"f1e3eb2593819aa0193393115c5bab9f73ec95f39c08bbcaf5e06f9662e2dc72","source":{"kind":"arxiv","id":"2001.05432","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.05432","created_at":"2026-07-05T04:36:45Z"},{"alias_kind":"arxiv_version","alias_value":"2001.05432v3","created_at":"2026-07-05T04:36:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.05432","created_at":"2026-07-05T04:36:45Z"},{"alias_kind":"pith_short_12","alias_value":"6HR6WJMTQGNK","created_at":"2026-07-05T04:36:45Z"},{"alias_kind":"pith_short_16","alias_value":"6HR6WJMTQGNKAGJT","created_at":"2026-07-05T04:36:45Z"},{"alias_kind":"pith_short_8","alias_value":"6HR6WJMT","created_at":"2026-07-05T04:36:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:6HR6WJMTQGNKAGJTSMIVYW5LT5","target":"record","payload":{"canonical_record":{"source":{"id":"2001.05432","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-01-15T16:59:36Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"dbb9c1064a0e07f846bd64cd3c6e645a86cec078d2914f2d94a14196236251ce","abstract_canon_sha256":"0c088c5b4f074c06e528f730ad0891f2c2f47e744b7da30d64cb9c672d4acd4a"},"schema_version":"1.0"},"canonical_sha256":"f1e3eb2593819aa0193393115c5bab9f73ec95f39c08bbcaf5e06f9662e2dc72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:36:45.004146Z","signature_b64":"ubhdMxaZRpZDqh25prDRgi6V2arwrlYbM2Dd8aFojEcBwoYSbgYefFxDLnIdlsSP8yiRehWjcsilMKrvKRvSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1e3eb2593819aa0193393115c5bab9f73ec95f39c08bbcaf5e06f9662e2dc72","last_reissued_at":"2026-07-05T04:36:45.003800Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:36:45.003800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2001.05432","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":"2026-07-05T04:36:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k53gNDFhM4X8nHbZ4Mr3TaysuhArAFH6lWCTkRg1eOJVzYuKIDONxnEQ3xACiHw3d/Qb73uOpCcJIILcqNkWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:54:48.225279Z"},"content_sha256":"d2aa48a18b1c33b966bcb58ce92cb9f6a5c4ddbde1d3bf5173b035e9ee66acb5","schema_version":"1.0","event_id":"sha256:d2aa48a18b1c33b966bcb58ce92cb9f6a5c4ddbde1d3bf5173b035e9ee66acb5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:6HR6WJMTQGNKAGJTSMIVYW5LT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homotopy theory of algebras of substitudes and their localisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"David White, Michael Batanin","submitted_at":"2020-01-15T16:59:36Z","abstract_excerpt":"We study the category of algebras of substitudes (also known to be equivalent to the regular patterns of Getzler) equipped with a (semi)model structure lifted from the model structure on the underlying presheaves. We are especially interested in the case when the model structure on presheaves is a Cisinski style localisation with respect to a proper Grothendieck fundamental localiser. For example, for $\\mathtt{W}=\\mathtt{W}_{\\infty}$ the minimal fundamental localiser, the local objects in such a localisation are locally constant presheaves, and local algebras of substitudes are exactly algebra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.05432","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.05432/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":"2026-07-05T04:36:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N7ZFA8GtIAfuQg5NFUQxi5xcFCf2TK9MNbbWmWUuxj5dfGHYiQ29RkyciKC1C4CGBNqVasKD+6YJHJ+0S8U/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:54:48.225655Z"},"content_sha256":"b64fba81f7b7188933fc1dbb8d3eed982b4aab96392999b4a9fe8dbba74c2684","schema_version":"1.0","event_id":"sha256:b64fba81f7b7188933fc1dbb8d3eed982b4aab96392999b4a9fe8dbba74c2684"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6HR6WJMTQGNKAGJTSMIVYW5LT5/bundle.json","state_url":"https://pith.science/pith/6HR6WJMTQGNKAGJTSMIVYW5LT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6HR6WJMTQGNKAGJTSMIVYW5LT5/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":"2026-08-21T01:54:48Z","links":{"resolver":"https://pith.science/pith/6HR6WJMTQGNKAGJTSMIVYW5LT5","bundle":"https://pith.science/pith/6HR6WJMTQGNKAGJTSMIVYW5LT5/bundle.json","state":"https://pith.science/pith/6HR6WJMTQGNKAGJTSMIVYW5LT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6HR6WJMTQGNKAGJTSMIVYW5LT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:6HR6WJMTQGNKAGJTSMIVYW5LT5","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":"0c088c5b4f074c06e528f730ad0891f2c2f47e744b7da30d64cb9c672d4acd4a","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-01-15T16:59:36Z","title_canon_sha256":"dbb9c1064a0e07f846bd64cd3c6e645a86cec078d2914f2d94a14196236251ce"},"schema_version":"1.0","source":{"id":"2001.05432","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.05432","created_at":"2026-07-05T04:36:45Z"},{"alias_kind":"arxiv_version","alias_value":"2001.05432v3","created_at":"2026-07-05T04:36:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.05432","created_at":"2026-07-05T04:36:45Z"},{"alias_kind":"pith_short_12","alias_value":"6HR6WJMTQGNK","created_at":"2026-07-05T04:36:45Z"},{"alias_kind":"pith_short_16","alias_value":"6HR6WJMTQGNKAGJT","created_at":"2026-07-05T04:36:45Z"},{"alias_kind":"pith_short_8","alias_value":"6HR6WJMT","created_at":"2026-07-05T04:36:45Z"}],"graph_snapshots":[{"event_id":"sha256:b64fba81f7b7188933fc1dbb8d3eed982b4aab96392999b4a9fe8dbba74c2684","target":"graph","created_at":"2026-07-05T04:36:45Z","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/2001.05432/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the category of algebras of substitudes (also known to be equivalent to the regular patterns of Getzler) equipped with a (semi)model structure lifted from the model structure on the underlying presheaves. We are especially interested in the case when the model structure on presheaves is a Cisinski style localisation with respect to a proper Grothendieck fundamental localiser. For example, for $\\mathtt{W}=\\mathtt{W}_{\\infty}$ the minimal fundamental localiser, the local objects in such a localisation are locally constant presheaves, and local algebras of substitudes are exactly algebra","authors_text":"David White, Michael Batanin","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-01-15T16:59:36Z","title":"Homotopy theory of algebras of substitudes and their localisation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.05432","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:d2aa48a18b1c33b966bcb58ce92cb9f6a5c4ddbde1d3bf5173b035e9ee66acb5","target":"record","created_at":"2026-07-05T04:36:45Z","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":"0c088c5b4f074c06e528f730ad0891f2c2f47e744b7da30d64cb9c672d4acd4a","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-01-15T16:59:36Z","title_canon_sha256":"dbb9c1064a0e07f846bd64cd3c6e645a86cec078d2914f2d94a14196236251ce"},"schema_version":"1.0","source":{"id":"2001.05432","kind":"arxiv","version":3}},"canonical_sha256":"f1e3eb2593819aa0193393115c5bab9f73ec95f39c08bbcaf5e06f9662e2dc72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1e3eb2593819aa0193393115c5bab9f73ec95f39c08bbcaf5e06f9662e2dc72","first_computed_at":"2026-07-05T04:36:45.003800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:36:45.003800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ubhdMxaZRpZDqh25prDRgi6V2arwrlYbM2Dd8aFojEcBwoYSbgYefFxDLnIdlsSP8yiRehWjcsilMKrvKRvSDg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:36:45.004146Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.05432","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2aa48a18b1c33b966bcb58ce92cb9f6a5c4ddbde1d3bf5173b035e9ee66acb5","sha256:b64fba81f7b7188933fc1dbb8d3eed982b4aab96392999b4a9fe8dbba74c2684"],"state_sha256":"6a877b67d69118b0d0bb4ad82fbf624be695e0ded49dd84f87670228a0dbb1b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mW0O2REQ6GWBoigJl/oNJd3JUtyLP1w1HvpwOuKaDpANLEtmKi1SeVJbnkFGkch5zw8mCCNZ2RcHUMVUQgRGBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T01:54:48.229049Z","bundle_sha256":"6a92f7be9ed48cb187209377b289490ecd10eb2fa38f906b5ad6a478599f7b88"}}