{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SOOGMW56VGBLOCSNMEHLN3Q6XV","short_pith_number":"pith:SOOGMW56","canonical_record":{"source":{"id":"2507.20037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-07-26T18:41:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"498bedf8e42603b2bd1a48c7dfda72c13f0cc6943329e17d2e3fff623e29f626","abstract_canon_sha256":"bd985b863893b380fef6d6a21dce4663937ba67b27be2f8802217719dbbee15b"},"schema_version":"1.0"},"canonical_sha256":"939c665bbea982b70a4d610eb6ee1ebd44c1e29f7cc93998b1cdff2d76d786df","source":{"kind":"arxiv","id":"2507.20037","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.20037","created_at":"2026-07-05T11:43:47Z"},{"alias_kind":"arxiv_version","alias_value":"2507.20037v1","created_at":"2026-07-05T11:43:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20037","created_at":"2026-07-05T11:43:47Z"},{"alias_kind":"pith_short_12","alias_value":"SOOGMW56VGBL","created_at":"2026-07-05T11:43:47Z"},{"alias_kind":"pith_short_16","alias_value":"SOOGMW56VGBLOCSN","created_at":"2026-07-05T11:43:47Z"},{"alias_kind":"pith_short_8","alias_value":"SOOGMW56","created_at":"2026-07-05T11:43:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SOOGMW56VGBLOCSNMEHLN3Q6XV","target":"record","payload":{"canonical_record":{"source":{"id":"2507.20037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-07-26T18:41:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"498bedf8e42603b2bd1a48c7dfda72c13f0cc6943329e17d2e3fff623e29f626","abstract_canon_sha256":"bd985b863893b380fef6d6a21dce4663937ba67b27be2f8802217719dbbee15b"},"schema_version":"1.0"},"canonical_sha256":"939c665bbea982b70a4d610eb6ee1ebd44c1e29f7cc93998b1cdff2d76d786df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:47.057466Z","signature_b64":"Bhf9/to90uF0ZlYpeTT2loWTdmcHAvOXsf4xvdfoxyRrwG+0J9ytL4RuBsOgp6ogUBaVJmgH/umDrEJYU8R2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"939c665bbea982b70a4d610eb6ee1ebd44c1e29f7cc93998b1cdff2d76d786df","last_reissued_at":"2026-07-05T11:43:47.056737Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:47.056737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.20037","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":"2026-07-05T11:43:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Z6UdK4f6VSpG3Lh5pPLTNMIe33WC8Fwo8yaRs/muP1yGtNyjwdhZCgv+742mroHQhHWUDZ4G/MTPJV1TYYsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:24:58.307172Z"},"content_sha256":"1b4fde75b04172cbce667bbfdac2efe715c4d183b8932d9475ff6556c368cbf6","schema_version":"1.0","event_id":"sha256:1b4fde75b04172cbce667bbfdac2efe715c4d183b8932d9475ff6556c368cbf6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SOOGMW56VGBLOCSNMEHLN3Q6XV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comparing the face rings of a boolean complex and its barycentric subdivision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Ben Blum-Smith, Sophie Marques","submitted_at":"2025-07-26T18:41:31Z","abstract_excerpt":"We consider the relationship between the Stanley-Reisner ring (a.k.a. face ring) of a simplicial or boolean complex $\\Delta$ and that of its barycentric subdivision. These rings share a distinguished parameter subring. S. Murai asked if they are isomorphic, equivariantly with respect to the automorphism group $\\operatorname{Aut}(\\Delta)$, as modules over this parameter subring. We show that, in general, the answer is no, but for Cohen-Macaulay complexes in characteristic coprime to $|\\operatorname{Aut}(\\Delta)|$, it is yes, and we give an explicit construction of an isomorphism. To give this c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20037","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/2507.20037/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":"2026-07-05T11:43:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sVQhngRO9OVIi6ZUkApn1w6ivD4f/DvfauN07jN+yPejrmGb6PeQUpu2MJYwqwhO3uk93JThFt4T/eJHbdzMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:24:58.308144Z"},"content_sha256":"99940348de9e5f9ea342f3f4ed98ff62e7c422dd181139cd52a0f0c73ff5a8e5","schema_version":"1.0","event_id":"sha256:99940348de9e5f9ea342f3f4ed98ff62e7c422dd181139cd52a0f0c73ff5a8e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SOOGMW56VGBLOCSNMEHLN3Q6XV/bundle.json","state_url":"https://pith.science/pith/SOOGMW56VGBLOCSNMEHLN3Q6XV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SOOGMW56VGBLOCSNMEHLN3Q6XV/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":"2026-08-13T17:24:58Z","links":{"resolver":"https://pith.science/pith/SOOGMW56VGBLOCSNMEHLN3Q6XV","bundle":"https://pith.science/pith/SOOGMW56VGBLOCSNMEHLN3Q6XV/bundle.json","state":"https://pith.science/pith/SOOGMW56VGBLOCSNMEHLN3Q6XV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SOOGMW56VGBLOCSNMEHLN3Q6XV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SOOGMW56VGBLOCSNMEHLN3Q6XV","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":"bd985b863893b380fef6d6a21dce4663937ba67b27be2f8802217719dbbee15b","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-07-26T18:41:31Z","title_canon_sha256":"498bedf8e42603b2bd1a48c7dfda72c13f0cc6943329e17d2e3fff623e29f626"},"schema_version":"1.0","source":{"id":"2507.20037","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.20037","created_at":"2026-07-05T11:43:47Z"},{"alias_kind":"arxiv_version","alias_value":"2507.20037v1","created_at":"2026-07-05T11:43:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20037","created_at":"2026-07-05T11:43:47Z"},{"alias_kind":"pith_short_12","alias_value":"SOOGMW56VGBL","created_at":"2026-07-05T11:43:47Z"},{"alias_kind":"pith_short_16","alias_value":"SOOGMW56VGBLOCSN","created_at":"2026-07-05T11:43:47Z"},{"alias_kind":"pith_short_8","alias_value":"SOOGMW56","created_at":"2026-07-05T11:43:47Z"}],"graph_snapshots":[{"event_id":"sha256:99940348de9e5f9ea342f3f4ed98ff62e7c422dd181139cd52a0f0c73ff5a8e5","target":"graph","created_at":"2026-07-05T11:43:47Z","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/2507.20037/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the relationship between the Stanley-Reisner ring (a.k.a. face ring) of a simplicial or boolean complex $\\Delta$ and that of its barycentric subdivision. These rings share a distinguished parameter subring. S. Murai asked if they are isomorphic, equivariantly with respect to the automorphism group $\\operatorname{Aut}(\\Delta)$, as modules over this parameter subring. We show that, in general, the answer is no, but for Cohen-Macaulay complexes in characteristic coprime to $|\\operatorname{Aut}(\\Delta)|$, it is yes, and we give an explicit construction of an isomorphism. To give this c","authors_text":"Ben Blum-Smith, Sophie Marques","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-07-26T18:41:31Z","title":"Comparing the face rings of a boolean complex and its barycentric subdivision"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20037","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":"sha256:1b4fde75b04172cbce667bbfdac2efe715c4d183b8932d9475ff6556c368cbf6","target":"record","created_at":"2026-07-05T11:43:47Z","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":"bd985b863893b380fef6d6a21dce4663937ba67b27be2f8802217719dbbee15b","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-07-26T18:41:31Z","title_canon_sha256":"498bedf8e42603b2bd1a48c7dfda72c13f0cc6943329e17d2e3fff623e29f626"},"schema_version":"1.0","source":{"id":"2507.20037","kind":"arxiv","version":1}},"canonical_sha256":"939c665bbea982b70a4d610eb6ee1ebd44c1e29f7cc93998b1cdff2d76d786df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"939c665bbea982b70a4d610eb6ee1ebd44c1e29f7cc93998b1cdff2d76d786df","first_computed_at":"2026-07-05T11:43:47.056737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:43:47.056737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bhf9/to90uF0ZlYpeTT2loWTdmcHAvOXsf4xvdfoxyRrwG+0J9ytL4RuBsOgp6ogUBaVJmgH/umDrEJYU8R2CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:43:47.057466Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.20037","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b4fde75b04172cbce667bbfdac2efe715c4d183b8932d9475ff6556c368cbf6","sha256:99940348de9e5f9ea342f3f4ed98ff62e7c422dd181139cd52a0f0c73ff5a8e5"],"state_sha256":"e95b0da0f92e8fe875390fbfb5a7d75accfa06714b9eb4adc88ebb37949c6595"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FUXSZU6ADZWkU4rfY0xKycv8BX2OueYYwrmLU5kl1dycqCF4Fyz0+5HJAglmdWt8OihV93Yc6jqpzsjKNKD2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T17:24:58.329933Z","bundle_sha256":"22cfba42144375acf58b70a5dc8831cb82a08b8562a00b9dff49c0b143b5e07f"}}