{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:3HAZRJNAX3ZJA3ADCQAXMXGUV2","short_pith_number":"pith:3HAZRJNA","canonical_record":{"source":{"id":"2311.02505","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2023-11-04T20:51:01Z","cross_cats_sorted":["math.CO","math.PR","math.RT"],"title_canon_sha256":"994812a3c7f69ef2bcba815deb7ad4345231de519e6f912e26661f1ac3a6414d","abstract_canon_sha256":"4d58f5c02926f0370f64c27f65117863e818ac741b2b36d53ec213b9cf5bee26"},"schema_version":"1.0"},"canonical_sha256":"d9c198a5a0bef2906c031401765cd4aebf3e567b482ba0e02fd4cb73aea2209a","source":{"kind":"arxiv","id":"2311.02505","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.02505","created_at":"2026-07-05T11:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"2311.02505v2","created_at":"2026-07-05T11:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.02505","created_at":"2026-07-05T11:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"3HAZRJNAX3ZJ","created_at":"2026-07-05T11:55:59Z"},{"alias_kind":"pith_short_16","alias_value":"3HAZRJNAX3ZJA3AD","created_at":"2026-07-05T11:55:59Z"},{"alias_kind":"pith_short_8","alias_value":"3HAZRJNA","created_at":"2026-07-05T11:55:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:3HAZRJNAX3ZJA3ADCQAXMXGUV2","target":"record","payload":{"canonical_record":{"source":{"id":"2311.02505","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2023-11-04T20:51:01Z","cross_cats_sorted":["math.CO","math.PR","math.RT"],"title_canon_sha256":"994812a3c7f69ef2bcba815deb7ad4345231de519e6f912e26661f1ac3a6414d","abstract_canon_sha256":"4d58f5c02926f0370f64c27f65117863e818ac741b2b36d53ec213b9cf5bee26"},"schema_version":"1.0"},"canonical_sha256":"d9c198a5a0bef2906c031401765cd4aebf3e567b482ba0e02fd4cb73aea2209a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:55:59.241367Z","signature_b64":"Jy5rUn31g8SVbBuR3NkOvE70D2AKvfiwJLs2kz102AsdKdpgYRyAmCrRZhCQ9h55TnPvpRIztM3R3RxffAlfBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9c198a5a0bef2906c031401765cd4aebf3e567b482ba0e02fd4cb73aea2209a","last_reissued_at":"2026-07-05T11:55:59.240930Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:55:59.240930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.02505","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hVhF70mUX1H8XBX4096xyqtC7C5WpflvrvePFpYLu2IM6ltAtCtVHBhseMEsCn/ZB0AmKLxQrr4RqXIZdwiDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T07:32:12.427388Z"},"content_sha256":"ea10beb73e5662d9084a7288f479f4ea4d7580b31cd5a6a13771aceb5265453f","schema_version":"1.0","event_id":"sha256:ea10beb73e5662d9084a7288f479f4ea4d7580b31cd5a6a13771aceb5265453f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:3HAZRJNAX3ZJA3ADCQAXMXGUV2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CO","math.PR","math.RT"],"primary_cat":"math.GR","authors_text":"Doron Puder, Gady Kozma, Gil Alon","submitted_at":"2023-11-04T20:51:01Z","abstract_excerpt":"In their celebrated paper (arXiv:0906.1238), Caputo, Liggett and Richthammer proved Aldous' conjecture and showed that for an arbitrary finite graph, the spectral gap of the interchange process is equal to the spectral gap of the underlying random walk. A crucial ingredient in the proof was the Octopus Inequality - a certain inequality of operators in the group ring $\\mathbb{R}[\\mathrm{Sym}_n]$ of the symmetric group. Here we generalize the Octopus Inequality and apply it to generalize the Caputo-Liggett-Richthammer Theorem to certain hypergraphs, proving some cases of a conjecture of Caputo."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.02505","kind":"arxiv","version":2},"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/2311.02505/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":"2026-07-05T11:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKtiiO+0QSSracqVA4wLIFXyvYDUgjm1wLeKWqtYEYCkizV/4vJY/+itVXVtMZpUtVEkOOVTbKnihMS8zYgNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T07:32:12.427975Z"},"content_sha256":"73f46b92d981b93246a6cb5ff4cb892197cabbc8f4bd27a640242975edf824b1","schema_version":"1.0","event_id":"sha256:73f46b92d981b93246a6cb5ff4cb892197cabbc8f4bd27a640242975edf824b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3HAZRJNAX3ZJA3ADCQAXMXGUV2/bundle.json","state_url":"https://pith.science/pith/3HAZRJNAX3ZJA3ADCQAXMXGUV2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3HAZRJNAX3ZJA3ADCQAXMXGUV2/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":"2026-08-15T07:32:12Z","links":{"resolver":"https://pith.science/pith/3HAZRJNAX3ZJA3ADCQAXMXGUV2","bundle":"https://pith.science/pith/3HAZRJNAX3ZJA3ADCQAXMXGUV2/bundle.json","state":"https://pith.science/pith/3HAZRJNAX3ZJA3ADCQAXMXGUV2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3HAZRJNAX3ZJA3ADCQAXMXGUV2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:3HAZRJNAX3ZJA3ADCQAXMXGUV2","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":"4d58f5c02926f0370f64c27f65117863e818ac741b2b36d53ec213b9cf5bee26","cross_cats_sorted":["math.CO","math.PR","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2023-11-04T20:51:01Z","title_canon_sha256":"994812a3c7f69ef2bcba815deb7ad4345231de519e6f912e26661f1ac3a6414d"},"schema_version":"1.0","source":{"id":"2311.02505","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.02505","created_at":"2026-07-05T11:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"2311.02505v2","created_at":"2026-07-05T11:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.02505","created_at":"2026-07-05T11:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"3HAZRJNAX3ZJ","created_at":"2026-07-05T11:55:59Z"},{"alias_kind":"pith_short_16","alias_value":"3HAZRJNAX3ZJA3AD","created_at":"2026-07-05T11:55:59Z"},{"alias_kind":"pith_short_8","alias_value":"3HAZRJNA","created_at":"2026-07-05T11:55:59Z"}],"graph_snapshots":[{"event_id":"sha256:73f46b92d981b93246a6cb5ff4cb892197cabbc8f4bd27a640242975edf824b1","target":"graph","created_at":"2026-07-05T11:55:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2311.02505/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In their celebrated paper (arXiv:0906.1238), Caputo, Liggett and Richthammer proved Aldous' conjecture and showed that for an arbitrary finite graph, the spectral gap of the interchange process is equal to the spectral gap of the underlying random walk. A crucial ingredient in the proof was the Octopus Inequality - a certain inequality of operators in the group ring $\\mathbb{R}[\\mathrm{Sym}_n]$ of the symmetric group. Here we generalize the Octopus Inequality and apply it to generalize the Caputo-Liggett-Richthammer Theorem to certain hypergraphs, proving some cases of a conjecture of Caputo.","authors_text":"Doron Puder, Gady Kozma, Gil Alon","cross_cats":["math.CO","math.PR","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2023-11-04T20:51:01Z","title":"On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.02505","kind":"arxiv","version":2},"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:ea10beb73e5662d9084a7288f479f4ea4d7580b31cd5a6a13771aceb5265453f","target":"record","created_at":"2026-07-05T11:55:59Z","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":"4d58f5c02926f0370f64c27f65117863e818ac741b2b36d53ec213b9cf5bee26","cross_cats_sorted":["math.CO","math.PR","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2023-11-04T20:51:01Z","title_canon_sha256":"994812a3c7f69ef2bcba815deb7ad4345231de519e6f912e26661f1ac3a6414d"},"schema_version":"1.0","source":{"id":"2311.02505","kind":"arxiv","version":2}},"canonical_sha256":"d9c198a5a0bef2906c031401765cd4aebf3e567b482ba0e02fd4cb73aea2209a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9c198a5a0bef2906c031401765cd4aebf3e567b482ba0e02fd4cb73aea2209a","first_computed_at":"2026-07-05T11:55:59.240930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:55:59.240930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jy5rUn31g8SVbBuR3NkOvE70D2AKvfiwJLs2kz102AsdKdpgYRyAmCrRZhCQ9h55TnPvpRIztM3R3RxffAlfBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:55:59.241367Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.02505","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea10beb73e5662d9084a7288f479f4ea4d7580b31cd5a6a13771aceb5265453f","sha256:73f46b92d981b93246a6cb5ff4cb892197cabbc8f4bd27a640242975edf824b1"],"state_sha256":"6afe2dcc2e749c1db4304647362dafb4c6a0b72db28cadd58cd1f8fd7fc85daa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ro+YyCMMbNOUKeagPn5Zj2L2FZ04fQmG48xZr1It7TvsNgD3sRkMkCELoldi+xEoPwLC50tlOyFQUrqJee4nCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T07:32:12.432256Z","bundle_sha256":"fba26cc5c4fe33492b98fbf4527e97f7dd01990c391f53d7681f2acd4e53ed84"}}