{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4XDYFYBU7TQQ3LBS75TDSG6LZK","short_pith_number":"pith:4XDYFYBU","canonical_record":{"source":{"id":"1504.04328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-16T18:27:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6dc8447e28b8b46e46c0e7940c167c71e6393ff270379401f67c0834d122567c","abstract_canon_sha256":"0c041f17db32b8070aa29c73b48c92a478ab17c2fd1862972087616187fbc083"},"schema_version":"1.0"},"canonical_sha256":"e5c782e034fce10dac32ff66391bcbcaa1b7bf33bacf97a5b5b1fbaca261dd67","source":{"kind":"arxiv","id":"1504.04328","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04328","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04328v1","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04328","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"4XDYFYBU7TQQ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4XDYFYBU7TQQ3LBS","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4XDYFYBU","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4XDYFYBU7TQQ3LBS75TDSG6LZK","target":"record","payload":{"canonical_record":{"source":{"id":"1504.04328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-16T18:27:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6dc8447e28b8b46e46c0e7940c167c71e6393ff270379401f67c0834d122567c","abstract_canon_sha256":"0c041f17db32b8070aa29c73b48c92a478ab17c2fd1862972087616187fbc083"},"schema_version":"1.0"},"canonical_sha256":"e5c782e034fce10dac32ff66391bcbcaa1b7bf33bacf97a5b5b1fbaca261dd67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:33.439203Z","signature_b64":"7AXbZ+UFSfhVW5C+m0as1sYuFc6fzNWzNeKrJz6/JWKkikN0g0Fp4BEOV52sOjPTp1WgQ2we36CG9rRhqecXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5c782e034fce10dac32ff66391bcbcaa1b7bf33bacf97a5b5b1fbaca261dd67","last_reissued_at":"2026-05-18T02:18:33.438574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:33.438574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.04328","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":"2026-05-18T02:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lTF4WGR+N5KB9Iupj2tHmv2tqN5vm5AIgnZr+rQbhldJ4GajcxvMrpuaVx0oP6i+yKQJEXUN0P4oq6xsN50+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:14:53.052732Z"},"content_sha256":"e81ee5601e23c85f062a323b18f62eac2524598a7648bb22575d916a3a737698","schema_version":"1.0","event_id":"sha256:e81ee5601e23c85f062a323b18f62eac2524598a7648bb22575d916a3a737698"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4XDYFYBU7TQQ3LBS75TDSG6LZK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimension filtration, sequential Cohen--Macaulayness and a new polynomial invariant of graded algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Afshin Goodarzi","submitted_at":"2015-04-16T18:27:20Z","abstract_excerpt":"Let $\\k$ be a field and let $A$ be a standard $\\mathbb{N}$-graded $\\k$-algebra. Using numerical information of some invariants in the primary decomposition of $0$ in $A$, namely the so called dimension filtration, we associate a bivariate polynomial $\\BW(A;t,w)$, that we call the Bj\\\"{o}rner--Wachs polynomial, to $A$.\n  It is shown that the Bj\\\"{o}rner--Wachs polynomial is an algebraic counterpart of the combinatorially defined $h$-triangle of finite simplicial complexes introduced by Bj\\\"{o}rner \\& Wachs. We provide a characterisation of sequentially Cohen--Macaulay algebras in terms of the e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04328","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":""},"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":"2026-05-18T02:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZeI2KH6bvMmtNO0ZZXbDqsxhJlcXLkds6dXN9EWABpL2OYq2PrGLaYfOgnffAWb/zdaHJn5UANew+COUh+EsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:14:53.053376Z"},"content_sha256":"830c38f2387a3dd7af110119d54e2f249903df1872903473e259d61e9030a707","schema_version":"1.0","event_id":"sha256:830c38f2387a3dd7af110119d54e2f249903df1872903473e259d61e9030a707"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XDYFYBU7TQQ3LBS75TDSG6LZK/bundle.json","state_url":"https://pith.science/pith/4XDYFYBU7TQQ3LBS75TDSG6LZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XDYFYBU7TQQ3LBS75TDSG6LZK/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":"2026-05-26T19:14:53Z","links":{"resolver":"https://pith.science/pith/4XDYFYBU7TQQ3LBS75TDSG6LZK","bundle":"https://pith.science/pith/4XDYFYBU7TQQ3LBS75TDSG6LZK/bundle.json","state":"https://pith.science/pith/4XDYFYBU7TQQ3LBS75TDSG6LZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XDYFYBU7TQQ3LBS75TDSG6LZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4XDYFYBU7TQQ3LBS75TDSG6LZK","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":"0c041f17db32b8070aa29c73b48c92a478ab17c2fd1862972087616187fbc083","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-16T18:27:20Z","title_canon_sha256":"6dc8447e28b8b46e46c0e7940c167c71e6393ff270379401f67c0834d122567c"},"schema_version":"1.0","source":{"id":"1504.04328","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04328","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04328v1","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04328","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"4XDYFYBU7TQQ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4XDYFYBU7TQQ3LBS","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4XDYFYBU","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:830c38f2387a3dd7af110119d54e2f249903df1872903473e259d61e9030a707","target":"graph","created_at":"2026-05-18T02:18:33Z","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":"Let $\\k$ be a field and let $A$ be a standard $\\mathbb{N}$-graded $\\k$-algebra. Using numerical information of some invariants in the primary decomposition of $0$ in $A$, namely the so called dimension filtration, we associate a bivariate polynomial $\\BW(A;t,w)$, that we call the Bj\\\"{o}rner--Wachs polynomial, to $A$.\n  It is shown that the Bj\\\"{o}rner--Wachs polynomial is an algebraic counterpart of the combinatorially defined $h$-triangle of finite simplicial complexes introduced by Bj\\\"{o}rner \\& Wachs. We provide a characterisation of sequentially Cohen--Macaulay algebras in terms of the e","authors_text":"Afshin Goodarzi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-16T18:27:20Z","title":"Dimension filtration, sequential Cohen--Macaulayness and a new polynomial invariant of graded algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04328","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:e81ee5601e23c85f062a323b18f62eac2524598a7648bb22575d916a3a737698","target":"record","created_at":"2026-05-18T02:18:33Z","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":"0c041f17db32b8070aa29c73b48c92a478ab17c2fd1862972087616187fbc083","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-16T18:27:20Z","title_canon_sha256":"6dc8447e28b8b46e46c0e7940c167c71e6393ff270379401f67c0834d122567c"},"schema_version":"1.0","source":{"id":"1504.04328","kind":"arxiv","version":1}},"canonical_sha256":"e5c782e034fce10dac32ff66391bcbcaa1b7bf33bacf97a5b5b1fbaca261dd67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5c782e034fce10dac32ff66391bcbcaa1b7bf33bacf97a5b5b1fbaca261dd67","first_computed_at":"2026-05-18T02:18:33.438574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:33.438574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7AXbZ+UFSfhVW5C+m0as1sYuFc6fzNWzNeKrJz6/JWKkikN0g0Fp4BEOV52sOjPTp1WgQ2we36CG9rRhqecXAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:33.439203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e81ee5601e23c85f062a323b18f62eac2524598a7648bb22575d916a3a737698","sha256:830c38f2387a3dd7af110119d54e2f249903df1872903473e259d61e9030a707"],"state_sha256":"c7be9aac65a496e4f786822aa134edc6611b72acb92b10ed3eb758300879f048"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8SyrJA8L8YK4kj+H3pedQV1BTyR17HYCLZddgkJWBSVrOVBvbf8oN9358GXlpD8NuEbBS5ght7ox/6kcICicBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:14:53.057386Z","bundle_sha256":"94734a29a3622505857135285c163262b84090653023585b0e59365cf690abf6"}}