{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:MS76GAC7P66AQB723DMYPFPIY3","short_pith_number":"pith:MS76GAC7","canonical_record":{"source":{"id":"2411.13294","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2024-11-20T13:04:54Z","cross_cats_sorted":["math.CO","math.GR","math.GT"],"title_canon_sha256":"2d8b1ef33ab0a68f2d0b65efd18e519114aed5ba9a104bf88034499349c4ad0d","abstract_canon_sha256":"6e43a48f4eaa07bace2232e6021cb12639317fe48fe60ae3d1144215188ebb30"},"schema_version":"1.0"},"canonical_sha256":"64bfe3005f7fbc0807fad8d98795e8c6d798dca73b44792a97c1ea5a358101ff","source":{"kind":"arxiv","id":"2411.13294","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13294","created_at":"2026-07-05T09:38:08Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13294v1","created_at":"2026-07-05T09:38:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13294","created_at":"2026-07-05T09:38:08Z"},{"alias_kind":"pith_short_12","alias_value":"MS76GAC7P66A","created_at":"2026-07-05T09:38:08Z"},{"alias_kind":"pith_short_16","alias_value":"MS76GAC7P66AQB72","created_at":"2026-07-05T09:38:08Z"},{"alias_kind":"pith_short_8","alias_value":"MS76GAC7","created_at":"2026-07-05T09:38:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:MS76GAC7P66AQB723DMYPFPIY3","target":"record","payload":{"canonical_record":{"source":{"id":"2411.13294","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2024-11-20T13:04:54Z","cross_cats_sorted":["math.CO","math.GR","math.GT"],"title_canon_sha256":"2d8b1ef33ab0a68f2d0b65efd18e519114aed5ba9a104bf88034499349c4ad0d","abstract_canon_sha256":"6e43a48f4eaa07bace2232e6021cb12639317fe48fe60ae3d1144215188ebb30"},"schema_version":"1.0"},"canonical_sha256":"64bfe3005f7fbc0807fad8d98795e8c6d798dca73b44792a97c1ea5a358101ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:38:08.163965Z","signature_b64":"nTgSihswBwEpzxfsPKbeKw8zlik9BGhqOtuwlLkajQq7QNZVWEzbxzokE3pK5LsgIy1A1ha39Fs95pW+CLb8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64bfe3005f7fbc0807fad8d98795e8c6d798dca73b44792a97c1ea5a358101ff","last_reissued_at":"2026-07-05T09:38:08.163511Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:38:08.163511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.13294","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":"2026-07-05T09:38:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sof0XfljKsrJ8YAyyDZCc7zxx0s7I/CIy+1GiM706M8mN/U7dFzsJcYpEqsGYCEfDDd0gFyLvtbTh8w9svmFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T07:46:58.770584Z"},"content_sha256":"060ab42995e9d3a1afad503a33f823eca2ff9d0d10f188d644dd68b1ce16261e","schema_version":"1.0","event_id":"sha256:060ab42995e9d3a1afad503a33f823eca2ff9d0d10f188d644dd68b1ce16261e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:MS76GAC7P66AQB723DMYPFPIY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological expanders, coarse geometry and thick embeddings of complexes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.GR","math.GT"],"primary_cat":"math.MG","authors_text":"David Hume","submitted_at":"2024-11-20T13:04:54Z","abstract_excerpt":"We quantify the topological expansion properties of bounded degree simplicial complexes in terms of a family of sublinear functions, in analogy with the separation profile of Benjamini-Schramm-Tim\\'ar for classical expansion of bounded degree graphs. We prove that, like the separation profile, these new invariants are monotone under regular maps between complexes satisfying appropriate higher connectivity assumptions. In the dimension $1$ case, we recover the cutwidth profile of Huang-Hume-Kelly-Lam. We also prove the seemingly new result that any $1$-dimensional topological expander necessari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13294","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.13294/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":"2026-07-05T09:38:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PwaavAACeXXa/EPRz7UlUPhQljf7iDw+o64PDsJ/xl5BpSeryTgNZV8PNXgVGEv9xmMQqaOqjXDsHEsY1ylgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T07:46:58.771092Z"},"content_sha256":"7a12dad3148f0b3611faa2bb7d3603e52be8cd4df453c05f53e6b56f52869314","schema_version":"1.0","event_id":"sha256:7a12dad3148f0b3611faa2bb7d3603e52be8cd4df453c05f53e6b56f52869314"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MS76GAC7P66AQB723DMYPFPIY3/bundle.json","state_url":"https://pith.science/pith/MS76GAC7P66AQB723DMYPFPIY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MS76GAC7P66AQB723DMYPFPIY3/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":"2026-08-13T07:46:58Z","links":{"resolver":"https://pith.science/pith/MS76GAC7P66AQB723DMYPFPIY3","bundle":"https://pith.science/pith/MS76GAC7P66AQB723DMYPFPIY3/bundle.json","state":"https://pith.science/pith/MS76GAC7P66AQB723DMYPFPIY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MS76GAC7P66AQB723DMYPFPIY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MS76GAC7P66AQB723DMYPFPIY3","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":"6e43a48f4eaa07bace2232e6021cb12639317fe48fe60ae3d1144215188ebb30","cross_cats_sorted":["math.CO","math.GR","math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2024-11-20T13:04:54Z","title_canon_sha256":"2d8b1ef33ab0a68f2d0b65efd18e519114aed5ba9a104bf88034499349c4ad0d"},"schema_version":"1.0","source":{"id":"2411.13294","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13294","created_at":"2026-07-05T09:38:08Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13294v1","created_at":"2026-07-05T09:38:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13294","created_at":"2026-07-05T09:38:08Z"},{"alias_kind":"pith_short_12","alias_value":"MS76GAC7P66A","created_at":"2026-07-05T09:38:08Z"},{"alias_kind":"pith_short_16","alias_value":"MS76GAC7P66AQB72","created_at":"2026-07-05T09:38:08Z"},{"alias_kind":"pith_short_8","alias_value":"MS76GAC7","created_at":"2026-07-05T09:38:08Z"}],"graph_snapshots":[{"event_id":"sha256:7a12dad3148f0b3611faa2bb7d3603e52be8cd4df453c05f53e6b56f52869314","target":"graph","created_at":"2026-07-05T09:38:08Z","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/2411.13294/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We quantify the topological expansion properties of bounded degree simplicial complexes in terms of a family of sublinear functions, in analogy with the separation profile of Benjamini-Schramm-Tim\\'ar for classical expansion of bounded degree graphs. We prove that, like the separation profile, these new invariants are monotone under regular maps between complexes satisfying appropriate higher connectivity assumptions. In the dimension $1$ case, we recover the cutwidth profile of Huang-Hume-Kelly-Lam. We also prove the seemingly new result that any $1$-dimensional topological expander necessari","authors_text":"David Hume","cross_cats":["math.CO","math.GR","math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2024-11-20T13:04:54Z","title":"Topological expanders, coarse geometry and thick embeddings of complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13294","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":"sha256:060ab42995e9d3a1afad503a33f823eca2ff9d0d10f188d644dd68b1ce16261e","target":"record","created_at":"2026-07-05T09:38:08Z","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":"6e43a48f4eaa07bace2232e6021cb12639317fe48fe60ae3d1144215188ebb30","cross_cats_sorted":["math.CO","math.GR","math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2024-11-20T13:04:54Z","title_canon_sha256":"2d8b1ef33ab0a68f2d0b65efd18e519114aed5ba9a104bf88034499349c4ad0d"},"schema_version":"1.0","source":{"id":"2411.13294","kind":"arxiv","version":1}},"canonical_sha256":"64bfe3005f7fbc0807fad8d98795e8c6d798dca73b44792a97c1ea5a358101ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64bfe3005f7fbc0807fad8d98795e8c6d798dca73b44792a97c1ea5a358101ff","first_computed_at":"2026-07-05T09:38:08.163511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:08.163511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nTgSihswBwEpzxfsPKbeKw8zlik9BGhqOtuwlLkajQq7QNZVWEzbxzokE3pK5LsgIy1A1ha39Fs95pW+CLb8Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:08.163965Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.13294","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:060ab42995e9d3a1afad503a33f823eca2ff9d0d10f188d644dd68b1ce16261e","sha256:7a12dad3148f0b3611faa2bb7d3603e52be8cd4df453c05f53e6b56f52869314"],"state_sha256":"98ff655550852344cad7c3565f4df6a073f78e8c507f1429de506c8eec07898b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YmDzfXzN9M+diykpuY3pKVo5ye3eN+v5twtfCL6MAn/qXuhMFo94dYMiIn57moQnxG0GAZjvWa+N5iocvgokBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T07:46:58.774352Z","bundle_sha256":"875ba87f3633054e867b90c6e5dc5dfc948bede5236222540d3c988457a4ad0f"}}