{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XEFULXRJGDUV2RNAU6S4DR2SGT","short_pith_number":"pith:XEFULXRJ","canonical_record":{"source":{"id":"1711.07107","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-19T23:58:32Z","cross_cats_sorted":[],"title_canon_sha256":"c85d6634080db7d22af1b4c8cbefd701fa7a3b77f67d4b6e5eba5fb5c42b7044","abstract_canon_sha256":"cd64361f4fc9dd6ef3a50a8b236cb5ae631a6e1fbd2a70bd91c61bfbe644219f"},"schema_version":"1.0"},"canonical_sha256":"b90b45de2930e95d45a0a7a5c1c75234f80c6349a3d61984e16bdc71b6b7b57e","source":{"kind":"arxiv","id":"1711.07107","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07107","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07107v1","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07107","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"XEFULXRJGDUV","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XEFULXRJGDUV2RNA","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XEFULXRJ","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XEFULXRJGDUV2RNAU6S4DR2SGT","target":"record","payload":{"canonical_record":{"source":{"id":"1711.07107","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-19T23:58:32Z","cross_cats_sorted":[],"title_canon_sha256":"c85d6634080db7d22af1b4c8cbefd701fa7a3b77f67d4b6e5eba5fb5c42b7044","abstract_canon_sha256":"cd64361f4fc9dd6ef3a50a8b236cb5ae631a6e1fbd2a70bd91c61bfbe644219f"},"schema_version":"1.0"},"canonical_sha256":"b90b45de2930e95d45a0a7a5c1c75234f80c6349a3d61984e16bdc71b6b7b57e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:59.994208Z","signature_b64":"7BnfBQCcb0prB5rYe+sf5Ab7I6PPzFrXrNaxOeG9sU+VitzEGCph7brzZvWwW9lQs72BqGc2zOR4jUILtAmzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b90b45de2930e95d45a0a7a5c1c75234f80c6349a3d61984e16bdc71b6b7b57e","last_reissued_at":"2026-05-17T23:44:59.993754Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:59.993754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.07107","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":"2026-05-17T23:44:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6OOO1AHZhCdFOXXhnWGyRWcdP7DQCHsU8PNR87qNVwy06C7fxyXlxTRSHJhlWgn519ZSqNVQuWtVsntng0npDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:05:11.087050Z"},"content_sha256":"828e0eb2a3dea3a80f5e6384bf23291339d4fa782b7c19bdfc9e475c3a6d8f13","schema_version":"1.0","event_id":"sha256:828e0eb2a3dea3a80f5e6384bf23291339d4fa782b7c19bdfc9e475c3a6d8f13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XEFULXRJGDUV2RNAU6S4DR2SGT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Occupants in simplicial complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Steffen Tillmann","submitted_at":"2017-11-19T23:58:32Z","abstract_excerpt":"Let $M$ be a smooth manifold and $K\\subset M$ be a simplicial complex of codimension at least 3. Functor calculus methods lead to a homotopical formula of $M\\setminus K$ in terms of spaces $M\\setminus T$ where $T$ is a finite subset of $K$. This is a generalization of the author's previous work with Michael Weiss where the subset $K$ is assumed to be a smooth submanifold of $M$ and uses his generalization of manifold calculus adapted for simplicial complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07107","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":"2026-05-17T23:44:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8tPIm3UsbX77Gwg/gH3v1CcZF0/IZ94wc9ywCnShdtkDvjOs6iEcoyn00IBPdM27MAlC1hsryVaEKRr3Yxf6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:05:11.087405Z"},"content_sha256":"a59b2b15778014a9a01463a194fdc5e5cbc9cc39b4a4adcca094b96577c04fd5","schema_version":"1.0","event_id":"sha256:a59b2b15778014a9a01463a194fdc5e5cbc9cc39b4a4adcca094b96577c04fd5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XEFULXRJGDUV2RNAU6S4DR2SGT/bundle.json","state_url":"https://pith.science/pith/XEFULXRJGDUV2RNAU6S4DR2SGT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XEFULXRJGDUV2RNAU6S4DR2SGT/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":"2026-06-24T20:05:11Z","links":{"resolver":"https://pith.science/pith/XEFULXRJGDUV2RNAU6S4DR2SGT","bundle":"https://pith.science/pith/XEFULXRJGDUV2RNAU6S4DR2SGT/bundle.json","state":"https://pith.science/pith/XEFULXRJGDUV2RNAU6S4DR2SGT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XEFULXRJGDUV2RNAU6S4DR2SGT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XEFULXRJGDUV2RNAU6S4DR2SGT","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":"cd64361f4fc9dd6ef3a50a8b236cb5ae631a6e1fbd2a70bd91c61bfbe644219f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-19T23:58:32Z","title_canon_sha256":"c85d6634080db7d22af1b4c8cbefd701fa7a3b77f67d4b6e5eba5fb5c42b7044"},"schema_version":"1.0","source":{"id":"1711.07107","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07107","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07107v1","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07107","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"XEFULXRJGDUV","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XEFULXRJGDUV2RNA","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XEFULXRJ","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:a59b2b15778014a9a01463a194fdc5e5cbc9cc39b4a4adcca094b96577c04fd5","target":"graph","created_at":"2026-05-17T23:44:59Z","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":"Let $M$ be a smooth manifold and $K\\subset M$ be a simplicial complex of codimension at least 3. Functor calculus methods lead to a homotopical formula of $M\\setminus K$ in terms of spaces $M\\setminus T$ where $T$ is a finite subset of $K$. This is a generalization of the author's previous work with Michael Weiss where the subset $K$ is assumed to be a smooth submanifold of $M$ and uses his generalization of manifold calculus adapted for simplicial complexes.","authors_text":"Steffen Tillmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-19T23:58:32Z","title":"Occupants in simplicial complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07107","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":"sha256:828e0eb2a3dea3a80f5e6384bf23291339d4fa782b7c19bdfc9e475c3a6d8f13","target":"record","created_at":"2026-05-17T23:44:59Z","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":"cd64361f4fc9dd6ef3a50a8b236cb5ae631a6e1fbd2a70bd91c61bfbe644219f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-19T23:58:32Z","title_canon_sha256":"c85d6634080db7d22af1b4c8cbefd701fa7a3b77f67d4b6e5eba5fb5c42b7044"},"schema_version":"1.0","source":{"id":"1711.07107","kind":"arxiv","version":1}},"canonical_sha256":"b90b45de2930e95d45a0a7a5c1c75234f80c6349a3d61984e16bdc71b6b7b57e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b90b45de2930e95d45a0a7a5c1c75234f80c6349a3d61984e16bdc71b6b7b57e","first_computed_at":"2026-05-17T23:44:59.993754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:59.993754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7BnfBQCcb0prB5rYe+sf5Ab7I6PPzFrXrNaxOeG9sU+VitzEGCph7brzZvWwW9lQs72BqGc2zOR4jUILtAmzCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:59.994208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.07107","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:828e0eb2a3dea3a80f5e6384bf23291339d4fa782b7c19bdfc9e475c3a6d8f13","sha256:a59b2b15778014a9a01463a194fdc5e5cbc9cc39b4a4adcca094b96577c04fd5"],"state_sha256":"d98c3d95d56caae957620ded660b683459f844ca426be64c4e15e91a33d8fb93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4S5pK/ntkpD3w1GNkDEcQpBXLqP31Kc/krg+cuRSr/vmcIFIaihYwgMkBpoiFIznZ4dysKOZ3H8S/TovsITICw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:05:11.089325Z","bundle_sha256":"3e0cf3fd729e801f1f90d3a1e3738e7c2d27f4ea4cf8b2ee17b365af99f912b4"}}