{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ERWNTAYA6HMTMXQLPDZQJ62U5W","short_pith_number":"pith:ERWNTAYA","canonical_record":{"source":{"id":"2410.09897","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-13T16:09:11Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"7199dbb210af21bce5d126c5d48eab3f7845c3788a94f272898711ba5616d1c2","abstract_canon_sha256":"18a92fa9daa7aa365ca16ac69a33659d85d0aceed0b6294987d309a8a40a22f7"},"schema_version":"1.0"},"canonical_sha256":"246cd98300f1d9365e0b78f304fb54ed99d87a2dc87ba4843766d6f62ec43b8f","source":{"kind":"arxiv","id":"2410.09897","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.09897","created_at":"2026-07-05T09:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"2410.09897v1","created_at":"2026-07-05T09:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.09897","created_at":"2026-07-05T09:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"ERWNTAYA6HMT","created_at":"2026-07-05T09:20:07Z"},{"alias_kind":"pith_short_16","alias_value":"ERWNTAYA6HMTMXQL","created_at":"2026-07-05T09:20:07Z"},{"alias_kind":"pith_short_8","alias_value":"ERWNTAYA","created_at":"2026-07-05T09:20:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ERWNTAYA6HMTMXQLPDZQJ62U5W","target":"record","payload":{"canonical_record":{"source":{"id":"2410.09897","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-13T16:09:11Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"7199dbb210af21bce5d126c5d48eab3f7845c3788a94f272898711ba5616d1c2","abstract_canon_sha256":"18a92fa9daa7aa365ca16ac69a33659d85d0aceed0b6294987d309a8a40a22f7"},"schema_version":"1.0"},"canonical_sha256":"246cd98300f1d9365e0b78f304fb54ed99d87a2dc87ba4843766d6f62ec43b8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:20:07.753279Z","signature_b64":"SOX3Ed89FfyVWjMtgxfuthpsM2qpkw3fWjchNTOYJn/tZTB2aq+yUgLabQNIJiAM0jsjpzn/Lg4jpTudIJWPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"246cd98300f1d9365e0b78f304fb54ed99d87a2dc87ba4843766d6f62ec43b8f","last_reissued_at":"2026-07-05T09:20:07.752745Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:20:07.752745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.09897","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":"2026-07-05T09:20:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VD1hbCju1j/JIpT4/lyMjltOoGATGdgMDzVaTK62nP3dGRJk/MhYw88s/NrvqdHvUhD4CuU2BhgT7aQYEOO7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T01:23:30.049176Z"},"content_sha256":"25a98fd8a8f612cefe6221c66b13341fb0ead01271671f8f54ac828dd41119a0","schema_version":"1.0","event_id":"sha256:25a98fd8a8f612cefe6221c66b13341fb0ead01271671f8f54ac828dd41119a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ERWNTAYA6HMTMXQLPDZQJ62U5W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some open problems on Coxeter groups and unimodality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.CO","authors_text":"Francesco Brenti","submitted_at":"2024-10-13T16:09:11Z","abstract_excerpt":"In this paper I present some open problems on Coxeter groups and unimodality, together with the main partial results, and computational evidence, that are known about them."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.09897","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/2410.09897/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":"2026-07-05T09:20:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J3RWnUISTgEUIbD2QjV3Xwh8BVhUmPpX6Z9f4PqEqGNqs9agABfNvaerdL/4rApgsrXPXfJYv7E2WzCHnY3TCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T01:23:30.049696Z"},"content_sha256":"c01c1212f1c50322fa0e3945732ee464628621c7b55c73d4a87ac0c85898f3c1","schema_version":"1.0","event_id":"sha256:c01c1212f1c50322fa0e3945732ee464628621c7b55c73d4a87ac0c85898f3c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERWNTAYA6HMTMXQLPDZQJ62U5W/bundle.json","state_url":"https://pith.science/pith/ERWNTAYA6HMTMXQLPDZQJ62U5W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERWNTAYA6HMTMXQLPDZQJ62U5W/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":"2026-08-14T01:23:30Z","links":{"resolver":"https://pith.science/pith/ERWNTAYA6HMTMXQLPDZQJ62U5W","bundle":"https://pith.science/pith/ERWNTAYA6HMTMXQLPDZQJ62U5W/bundle.json","state":"https://pith.science/pith/ERWNTAYA6HMTMXQLPDZQJ62U5W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERWNTAYA6HMTMXQLPDZQJ62U5W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ERWNTAYA6HMTMXQLPDZQJ62U5W","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":"18a92fa9daa7aa365ca16ac69a33659d85d0aceed0b6294987d309a8a40a22f7","cross_cats_sorted":["math.GR","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-13T16:09:11Z","title_canon_sha256":"7199dbb210af21bce5d126c5d48eab3f7845c3788a94f272898711ba5616d1c2"},"schema_version":"1.0","source":{"id":"2410.09897","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.09897","created_at":"2026-07-05T09:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"2410.09897v1","created_at":"2026-07-05T09:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.09897","created_at":"2026-07-05T09:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"ERWNTAYA6HMT","created_at":"2026-07-05T09:20:07Z"},{"alias_kind":"pith_short_16","alias_value":"ERWNTAYA6HMTMXQL","created_at":"2026-07-05T09:20:07Z"},{"alias_kind":"pith_short_8","alias_value":"ERWNTAYA","created_at":"2026-07-05T09:20:07Z"}],"graph_snapshots":[{"event_id":"sha256:c01c1212f1c50322fa0e3945732ee464628621c7b55c73d4a87ac0c85898f3c1","target":"graph","created_at":"2026-07-05T09:20:07Z","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/2410.09897/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper I present some open problems on Coxeter groups and unimodality, together with the main partial results, and computational evidence, that are known about them.","authors_text":"Francesco Brenti","cross_cats":["math.GR","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-13T16:09:11Z","title":"Some open problems on Coxeter groups and unimodality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.09897","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":"sha256:25a98fd8a8f612cefe6221c66b13341fb0ead01271671f8f54ac828dd41119a0","target":"record","created_at":"2026-07-05T09:20:07Z","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":"18a92fa9daa7aa365ca16ac69a33659d85d0aceed0b6294987d309a8a40a22f7","cross_cats_sorted":["math.GR","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-13T16:09:11Z","title_canon_sha256":"7199dbb210af21bce5d126c5d48eab3f7845c3788a94f272898711ba5616d1c2"},"schema_version":"1.0","source":{"id":"2410.09897","kind":"arxiv","version":1}},"canonical_sha256":"246cd98300f1d9365e0b78f304fb54ed99d87a2dc87ba4843766d6f62ec43b8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"246cd98300f1d9365e0b78f304fb54ed99d87a2dc87ba4843766d6f62ec43b8f","first_computed_at":"2026-07-05T09:20:07.752745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:20:07.752745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SOX3Ed89FfyVWjMtgxfuthpsM2qpkw3fWjchNTOYJn/tZTB2aq+yUgLabQNIJiAM0jsjpzn/Lg4jpTudIJWPCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:20:07.753279Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.09897","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25a98fd8a8f612cefe6221c66b13341fb0ead01271671f8f54ac828dd41119a0","sha256:c01c1212f1c50322fa0e3945732ee464628621c7b55c73d4a87ac0c85898f3c1"],"state_sha256":"cbd7569e1830951cb4dc889e77747ac1260ae8405aaa32b822ade2882301f06c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EucE/s3cH5MADXz2Go15/zdH0cTSGVuq8WKvdeJbC8LJA8+j2Ynqfmfzn3EywEqSg4QfTG0WB7Hn/eALl07xAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T01:23:30.055248Z","bundle_sha256":"0a5513ee323d00198cbd8d9cf1baac4e052229c9ed41bdb38255b12b5fb41fdd"}}