{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CJHC56ZQGVQ4FB44ZFR5U4VIVK","short_pith_number":"pith:CJHC56ZQ","canonical_record":{"source":{"id":"1412.7408","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-23T15:40:44Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"3150b26e6ab49d19c3aa644a561816233182a78c292d93e65a383bedaee1dd87","abstract_canon_sha256":"b92acfdf0257bb65c2ead2ffbe4f03284960f56024bbaab12d0a08ae4b0a1d22"},"schema_version":"1.0"},"canonical_sha256":"124e2efb303561c2879cc963da72a8aa8e8d6da2458eaabc51de51c71383674f","source":{"kind":"arxiv","id":"1412.7408","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7408","created_at":"2026-05-18T01:11:38Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7408v3","created_at":"2026-05-18T01:11:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7408","created_at":"2026-05-18T01:11:38Z"},{"alias_kind":"pith_short_12","alias_value":"CJHC56ZQGVQ4","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CJHC56ZQGVQ4FB44","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CJHC56ZQ","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CJHC56ZQGVQ4FB44ZFR5U4VIVK","target":"record","payload":{"canonical_record":{"source":{"id":"1412.7408","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-23T15:40:44Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"3150b26e6ab49d19c3aa644a561816233182a78c292d93e65a383bedaee1dd87","abstract_canon_sha256":"b92acfdf0257bb65c2ead2ffbe4f03284960f56024bbaab12d0a08ae4b0a1d22"},"schema_version":"1.0"},"canonical_sha256":"124e2efb303561c2879cc963da72a8aa8e8d6da2458eaabc51de51c71383674f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:38.796365Z","signature_b64":"Dx5J7nHTQdlL5kTFOCML8/Ls9BPcStxMZUfDE1eDAJPA39Nk7Iv3FK3io2bFdWKlI+pRVJejng6TNEpUde60DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"124e2efb303561c2879cc963da72a8aa8e8d6da2458eaabc51de51c71383674f","last_reissued_at":"2026-05-18T01:11:38.796001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:38.796001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.7408","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uhlZpze71Wf6m1C0fwv517jQZpvI07EvxQZoAF3kO0RMKrotKkZof51RvBbAUYvSxgEeEaeG4s4NTZDJVx/dBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:37:07.451370Z"},"content_sha256":"ba2908bb1273617fe1b4eafce1e45b2b1c86d308f0450f71c0ad19a7398cfd7c","schema_version":"1.0","event_id":"sha256:ba2908bb1273617fe1b4eafce1e45b2b1c86d308f0450f71c0ad19a7398cfd7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CJHC56ZQGVQ4FB44ZFR5U4VIVK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Kazhdan-Lusztig polynomial of a matroid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.CO","authors_text":"Ben Elias, Max Wakefield, Nicholas Proudfoot","submitted_at":"2014-12-23T15:40:44Z","abstract_excerpt":"We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M, in analogy with Kazhdan-Lusztig polynomials in representation theory. We conjecture that the coefficients are always non-negative, and we prove this conjecture for representable matroids by interpreting our polynomials as intersection cohomology Poincare polynomials. We also introduce a q-deformation of the Mobius algebra of M, and use our polynomials to define a special basis for this deformation, analogous to the canonical basis of the Hecke algebra. We conjecture that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7408","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:11:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DP65cpRiS+DklSpYFccO0n23xbEYAaZhUtNxqNiQaNO4tiOIQYUz6worKciery68MRwMjqxA/2rmRCJpYQ8gDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:37:07.452019Z"},"content_sha256":"8fd6b84d66bd6c455ad59dedb77337d42adec58d79f9843c6a0e34d7eed437d9","schema_version":"1.0","event_id":"sha256:8fd6b84d66bd6c455ad59dedb77337d42adec58d79f9843c6a0e34d7eed437d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJHC56ZQGVQ4FB44ZFR5U4VIVK/bundle.json","state_url":"https://pith.science/pith/CJHC56ZQGVQ4FB44ZFR5U4VIVK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJHC56ZQGVQ4FB44ZFR5U4VIVK/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":"2026-06-06T18:37:07Z","links":{"resolver":"https://pith.science/pith/CJHC56ZQGVQ4FB44ZFR5U4VIVK","bundle":"https://pith.science/pith/CJHC56ZQGVQ4FB44ZFR5U4VIVK/bundle.json","state":"https://pith.science/pith/CJHC56ZQGVQ4FB44ZFR5U4VIVK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJHC56ZQGVQ4FB44ZFR5U4VIVK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CJHC56ZQGVQ4FB44ZFR5U4VIVK","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":"b92acfdf0257bb65c2ead2ffbe4f03284960f56024bbaab12d0a08ae4b0a1d22","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-23T15:40:44Z","title_canon_sha256":"3150b26e6ab49d19c3aa644a561816233182a78c292d93e65a383bedaee1dd87"},"schema_version":"1.0","source":{"id":"1412.7408","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7408","created_at":"2026-05-18T01:11:38Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7408v3","created_at":"2026-05-18T01:11:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7408","created_at":"2026-05-18T01:11:38Z"},{"alias_kind":"pith_short_12","alias_value":"CJHC56ZQGVQ4","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CJHC56ZQGVQ4FB44","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CJHC56ZQ","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:8fd6b84d66bd6c455ad59dedb77337d42adec58d79f9843c6a0e34d7eed437d9","target":"graph","created_at":"2026-05-18T01:11:38Z","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"},"paper":{"abstract_excerpt":"We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M, in analogy with Kazhdan-Lusztig polynomials in representation theory. We conjecture that the coefficients are always non-negative, and we prove this conjecture for representable matroids by interpreting our polynomials as intersection cohomology Poincare polynomials. We also introduce a q-deformation of the Mobius algebra of M, and use our polynomials to define a special basis for this deformation, analogous to the canonical basis of the Hecke algebra. We conjecture that t","authors_text":"Ben Elias, Max Wakefield, Nicholas Proudfoot","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-23T15:40:44Z","title":"The Kazhdan-Lusztig polynomial of a matroid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7408","kind":"arxiv","version":3},"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:ba2908bb1273617fe1b4eafce1e45b2b1c86d308f0450f71c0ad19a7398cfd7c","target":"record","created_at":"2026-05-18T01:11:38Z","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":"b92acfdf0257bb65c2ead2ffbe4f03284960f56024bbaab12d0a08ae4b0a1d22","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-23T15:40:44Z","title_canon_sha256":"3150b26e6ab49d19c3aa644a561816233182a78c292d93e65a383bedaee1dd87"},"schema_version":"1.0","source":{"id":"1412.7408","kind":"arxiv","version":3}},"canonical_sha256":"124e2efb303561c2879cc963da72a8aa8e8d6da2458eaabc51de51c71383674f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"124e2efb303561c2879cc963da72a8aa8e8d6da2458eaabc51de51c71383674f","first_computed_at":"2026-05-18T01:11:38.796001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:38.796001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dx5J7nHTQdlL5kTFOCML8/Ls9BPcStxMZUfDE1eDAJPA39Nk7Iv3FK3io2bFdWKlI+pRVJejng6TNEpUde60DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:38.796365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7408","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba2908bb1273617fe1b4eafce1e45b2b1c86d308f0450f71c0ad19a7398cfd7c","sha256:8fd6b84d66bd6c455ad59dedb77337d42adec58d79f9843c6a0e34d7eed437d9"],"state_sha256":"3b2026b217d5f476eb91554f722ec26c97995f689c10626cfda27669a7ab6ca6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6W39/sneW14O2dwBH5llBuqQZ7Ke4lMiwN3twGVlLGuF9nLfpfif+/eSQi8l2VaQAdfMwKfZ8fwJSIC17z8qDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:37:07.455903Z","bundle_sha256":"ef7b9a6d5ec31766ab780cf70ce895dd69431844d948e34b26c0c84080a13a92"}}