{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2WC3WNSBKIQEVY5UBJHZQEKMFH","short_pith_number":"pith:2WC3WNSB","canonical_record":{"source":{"id":"2506.08858","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T14:48:25Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"9bef7945afa7a96c54643a911437988ecc04c10fae6cf3c72101e9eaec0ab7e2","abstract_canon_sha256":"1a7b80dae66285e8b56b9fda72475df292d04af7b412f16871438200f08e9284"},"schema_version":"1.0"},"canonical_sha256":"d585bb364152204ae3b40a4f98114c29f0dc7427d1e34b61303ccaca7cd3b2ca","source":{"kind":"arxiv","id":"2506.08858","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08858","created_at":"2026-07-05T11:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08858v1","created_at":"2026-07-05T11:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08858","created_at":"2026-07-05T11:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"2WC3WNSBKIQE","created_at":"2026-07-05T11:19:14Z"},{"alias_kind":"pith_short_16","alias_value":"2WC3WNSBKIQEVY5U","created_at":"2026-07-05T11:19:14Z"},{"alias_kind":"pith_short_8","alias_value":"2WC3WNSB","created_at":"2026-07-05T11:19:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2WC3WNSBKIQEVY5UBJHZQEKMFH","target":"record","payload":{"canonical_record":{"source":{"id":"2506.08858","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T14:48:25Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"9bef7945afa7a96c54643a911437988ecc04c10fae6cf3c72101e9eaec0ab7e2","abstract_canon_sha256":"1a7b80dae66285e8b56b9fda72475df292d04af7b412f16871438200f08e9284"},"schema_version":"1.0"},"canonical_sha256":"d585bb364152204ae3b40a4f98114c29f0dc7427d1e34b61303ccaca7cd3b2ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:14.294459Z","signature_b64":"Xknogn+i/uEKE0Ljn+rpRipcFD4EB4DYGDA+1vFu23oVyNEQ0hh4BPesNFGFbrAC0F5nr15wTP/ATDflfbRcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d585bb364152204ae3b40a4f98114c29f0dc7427d1e34b61303ccaca7cd3b2ca","last_reissued_at":"2026-07-05T11:19:14.294042Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:14.294042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.08858","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":"2026-07-05T11:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qLi0oRcWVSh4nScUoTkGa/mMROC+Vgz62R3tzHnaHKtH03yr1a++sZSDuidykVA+9BMMl3xAXtupRQLAOqiSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:54:34.165608Z"},"content_sha256":"429350313558e30bb08eec1941a36e02ba7118524a2fa42cb8c82837457d4867","schema_version":"1.0","event_id":"sha256:429350313558e30bb08eec1941a36e02ba7118524a2fa42cb8c82837457d4867"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2WC3WNSBKIQEVY5UBJHZQEKMFH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Mikhail Gorsky, Nicholas J. Williams","submitted_at":"2025-06-10T14:48:25Z","abstract_excerpt":"We study preorders on (equivalence classes of) maximal chains in the general context of polygonal lattices endowed with suitably nice edge labellings. We show that, given a quotient of polygonal lattices, such edge labellings descend to the quotient, and that there is an induced order-preserving surjective map on the preordered sets of equivalence classes of maximal chains. Under a natural condition ensuring that the domain is a poset, the map is a contraction of preordered sets. We apply this to lattices of regions of simplicial hyperplane arrangements, where the preorders are partial orders,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08858","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/2506.08858/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":"2026-07-05T11:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S2RdkkaKyDU/1UID4AFU1+ECqJjakBJgp3aIGtEzDAdgNY/KmI9yMBTwWIG9UU4R7QHev5nH0xfoiAO8izGUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:54:34.166371Z"},"content_sha256":"229ec05ed7a821a480ec1d65cc81123e81d4ce6a5dfa234dade75f5db31e5540","schema_version":"1.0","event_id":"sha256:229ec05ed7a821a480ec1d65cc81123e81d4ce6a5dfa234dade75f5db31e5540"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2WC3WNSBKIQEVY5UBJHZQEKMFH/bundle.json","state_url":"https://pith.science/pith/2WC3WNSBKIQEVY5UBJHZQEKMFH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2WC3WNSBKIQEVY5UBJHZQEKMFH/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":"2026-08-09T07:54:34Z","links":{"resolver":"https://pith.science/pith/2WC3WNSBKIQEVY5UBJHZQEKMFH","bundle":"https://pith.science/pith/2WC3WNSBKIQEVY5UBJHZQEKMFH/bundle.json","state":"https://pith.science/pith/2WC3WNSBKIQEVY5UBJHZQEKMFH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2WC3WNSBKIQEVY5UBJHZQEKMFH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2WC3WNSBKIQEVY5UBJHZQEKMFH","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":"1a7b80dae66285e8b56b9fda72475df292d04af7b412f16871438200f08e9284","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T14:48:25Z","title_canon_sha256":"9bef7945afa7a96c54643a911437988ecc04c10fae6cf3c72101e9eaec0ab7e2"},"schema_version":"1.0","source":{"id":"2506.08858","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08858","created_at":"2026-07-05T11:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08858v1","created_at":"2026-07-05T11:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08858","created_at":"2026-07-05T11:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"2WC3WNSBKIQE","created_at":"2026-07-05T11:19:14Z"},{"alias_kind":"pith_short_16","alias_value":"2WC3WNSBKIQEVY5U","created_at":"2026-07-05T11:19:14Z"},{"alias_kind":"pith_short_8","alias_value":"2WC3WNSB","created_at":"2026-07-05T11:19:14Z"}],"graph_snapshots":[{"event_id":"sha256:229ec05ed7a821a480ec1d65cc81123e81d4ce6a5dfa234dade75f5db31e5540","target":"graph","created_at":"2026-07-05T11:19:14Z","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/2506.08858/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study preorders on (equivalence classes of) maximal chains in the general context of polygonal lattices endowed with suitably nice edge labellings. We show that, given a quotient of polygonal lattices, such edge labellings descend to the quotient, and that there is an induced order-preserving surjective map on the preordered sets of equivalence classes of maximal chains. Under a natural condition ensuring that the domain is a poset, the map is a contraction of preordered sets. We apply this to lattices of regions of simplicial hyperplane arrangements, where the preorders are partial orders,","authors_text":"Mikhail Gorsky, Nicholas J. Williams","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T14:48:25Z","title":"Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08858","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":"sha256:429350313558e30bb08eec1941a36e02ba7118524a2fa42cb8c82837457d4867","target":"record","created_at":"2026-07-05T11:19:14Z","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":"1a7b80dae66285e8b56b9fda72475df292d04af7b412f16871438200f08e9284","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T14:48:25Z","title_canon_sha256":"9bef7945afa7a96c54643a911437988ecc04c10fae6cf3c72101e9eaec0ab7e2"},"schema_version":"1.0","source":{"id":"2506.08858","kind":"arxiv","version":1}},"canonical_sha256":"d585bb364152204ae3b40a4f98114c29f0dc7427d1e34b61303ccaca7cd3b2ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d585bb364152204ae3b40a4f98114c29f0dc7427d1e34b61303ccaca7cd3b2ca","first_computed_at":"2026-07-05T11:19:14.294042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:19:14.294042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xknogn+i/uEKE0Ljn+rpRipcFD4EB4DYGDA+1vFu23oVyNEQ0hh4BPesNFGFbrAC0F5nr15wTP/ATDflfbRcBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:19:14.294459Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.08858","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:429350313558e30bb08eec1941a36e02ba7118524a2fa42cb8c82837457d4867","sha256:229ec05ed7a821a480ec1d65cc81123e81d4ce6a5dfa234dade75f5db31e5540"],"state_sha256":"6362e695a286bb6f2239044dfd93601a3cf40ecf6f10813a5dfd3885b2823c58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a/vVPx9TmufaW7bHHakNOc4Vmzg6CvxfRcbctDEoZtr2YcEnHnvXmcsBdmjpRHzbU58v5yUApzVmeR2e0/CuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:54:34.171236Z","bundle_sha256":"1c1e050801567e8b3758d2664aa6d8d527c218243d9604ea4705a166caf8f474"}}