{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YPJT6ZUKG4GXT5VRM6BGXIR5VA","short_pith_number":"pith:YPJT6ZUK","canonical_record":{"source":{"id":"1302.1039","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-05T14:04:17Z","cross_cats_sorted":[],"title_canon_sha256":"b1331f09a951b8ca673e84a13cd6c3a0637247d66157eeff1f396f8426fe968b","abstract_canon_sha256":"fea2ed8bf27060d04c4d9e2676e8fbfdfc49529892f433ad1b5dffdcfd99fbf1"},"schema_version":"1.0"},"canonical_sha256":"c3d33f668a370d79f6b167826ba23da818aa79d65e031ba122cb661c77629b59","source":{"kind":"arxiv","id":"1302.1039","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1039","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1039v4","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1039","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"YPJT6ZUKG4GX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YPJT6ZUKG4GXT5VR","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YPJT6ZUK","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YPJT6ZUKG4GXT5VRM6BGXIR5VA","target":"record","payload":{"canonical_record":{"source":{"id":"1302.1039","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-05T14:04:17Z","cross_cats_sorted":[],"title_canon_sha256":"b1331f09a951b8ca673e84a13cd6c3a0637247d66157eeff1f396f8426fe968b","abstract_canon_sha256":"fea2ed8bf27060d04c4d9e2676e8fbfdfc49529892f433ad1b5dffdcfd99fbf1"},"schema_version":"1.0"},"canonical_sha256":"c3d33f668a370d79f6b167826ba23da818aa79d65e031ba122cb661c77629b59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:04.306410Z","signature_b64":"1R0/+RbUdTZghtrBpBDbHxD9pkbfeetR57ccMNAoRBLSts5HKCRUd6amZ8KI7VivlJiHbjFWkQ8DTpUMMGLZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3d33f668a370d79f6b167826ba23da818aa79d65e031ba122cb661c77629b59","last_reissued_at":"2026-05-18T03:08:04.305841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:04.305841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.1039","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m7fFk1LoHs7cqQ4LYFH0lsmVniQXvzzbm4XgWtOvEpFIgrqz9lIXNtGqV3RjU60a/lrU2+jYFYOyoHj5JrA/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:40:10.697093Z"},"content_sha256":"5ba2514b450dfaecebcabc101a9c0348e2c28b1874619e8e89f9a42d8b6c2ac4","schema_version":"1.0","event_id":"sha256:5ba2514b450dfaecebcabc101a9c0348e2c28b1874619e8e89f9a42d8b6c2ac4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YPJT6ZUKG4GXT5VRM6BGXIR5VA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How to partition or count an abstract simplicial complex, given its facets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marcel Wild","submitted_at":"2013-02-05T14:04:17Z","abstract_excerpt":"Given are the facets of an abstract (finite) simplicial complex SC. We show how to partition SC into few pieces, each one compactly encoded by the use of wildcards. Such a representation is useful for the optimization of a target function SC -> Z, as well as in combinatorial commutative algebra and Frequent Set Mining. Merely calculating the face-numbers of SC can be done faster than partitioning SC. Our method compares favorably to inclusion-exclusion and binary decision diagram"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1039","kind":"arxiv","version":4},"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":"2026-05-18T03:08:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qbftLlhoTIgx52a8PdCr09nB6JDPxDi8PqM4fv0z9s9k+l3gbWV/9M/XPkaEeLPZVLheIuBYoXCsRVVdTWqjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:40:10.697450Z"},"content_sha256":"5c53b9bb038100007be9f18506b8cc3c1247dda46ff5ce9e19b55196754beb7d","schema_version":"1.0","event_id":"sha256:5c53b9bb038100007be9f18506b8cc3c1247dda46ff5ce9e19b55196754beb7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YPJT6ZUKG4GXT5VRM6BGXIR5VA/bundle.json","state_url":"https://pith.science/pith/YPJT6ZUKG4GXT5VRM6BGXIR5VA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YPJT6ZUKG4GXT5VRM6BGXIR5VA/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":"2026-05-27T15:40:10Z","links":{"resolver":"https://pith.science/pith/YPJT6ZUKG4GXT5VRM6BGXIR5VA","bundle":"https://pith.science/pith/YPJT6ZUKG4GXT5VRM6BGXIR5VA/bundle.json","state":"https://pith.science/pith/YPJT6ZUKG4GXT5VRM6BGXIR5VA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YPJT6ZUKG4GXT5VRM6BGXIR5VA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YPJT6ZUKG4GXT5VRM6BGXIR5VA","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":"fea2ed8bf27060d04c4d9e2676e8fbfdfc49529892f433ad1b5dffdcfd99fbf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-05T14:04:17Z","title_canon_sha256":"b1331f09a951b8ca673e84a13cd6c3a0637247d66157eeff1f396f8426fe968b"},"schema_version":"1.0","source":{"id":"1302.1039","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1039","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1039v4","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1039","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"YPJT6ZUKG4GX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YPJT6ZUKG4GXT5VR","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YPJT6ZUK","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:5c53b9bb038100007be9f18506b8cc3c1247dda46ff5ce9e19b55196754beb7d","target":"graph","created_at":"2026-05-18T03:08:04Z","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":"Given are the facets of an abstract (finite) simplicial complex SC. We show how to partition SC into few pieces, each one compactly encoded by the use of wildcards. Such a representation is useful for the optimization of a target function SC -> Z, as well as in combinatorial commutative algebra and Frequent Set Mining. Merely calculating the face-numbers of SC can be done faster than partitioning SC. Our method compares favorably to inclusion-exclusion and binary decision diagram","authors_text":"Marcel Wild","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-05T14:04:17Z","title":"How to partition or count an abstract simplicial complex, given its facets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1039","kind":"arxiv","version":4},"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":"sha256:5ba2514b450dfaecebcabc101a9c0348e2c28b1874619e8e89f9a42d8b6c2ac4","target":"record","created_at":"2026-05-18T03:08:04Z","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":"fea2ed8bf27060d04c4d9e2676e8fbfdfc49529892f433ad1b5dffdcfd99fbf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-05T14:04:17Z","title_canon_sha256":"b1331f09a951b8ca673e84a13cd6c3a0637247d66157eeff1f396f8426fe968b"},"schema_version":"1.0","source":{"id":"1302.1039","kind":"arxiv","version":4}},"canonical_sha256":"c3d33f668a370d79f6b167826ba23da818aa79d65e031ba122cb661c77629b59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3d33f668a370d79f6b167826ba23da818aa79d65e031ba122cb661c77629b59","first_computed_at":"2026-05-18T03:08:04.305841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:04.305841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1R0/+RbUdTZghtrBpBDbHxD9pkbfeetR57ccMNAoRBLSts5HKCRUd6amZ8KI7VivlJiHbjFWkQ8DTpUMMGLZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:04.306410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1039","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ba2514b450dfaecebcabc101a9c0348e2c28b1874619e8e89f9a42d8b6c2ac4","sha256:5c53b9bb038100007be9f18506b8cc3c1247dda46ff5ce9e19b55196754beb7d"],"state_sha256":"12f9e79fcf121ab797f72987e4771073841478b6cf0159e9c53f7b1d9363d85b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wdNC0pBtKgi+a2YXEp4C6iMDGxNmi9eoj4aaud1RV65aGQh+MUn0rwECQ33htavkkmIq/Q8DS93r/vo75urGAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:40:10.699612Z","bundle_sha256":"b130b6cd307620944d98579bf544dc3ae105a412d4c0c9deca37c6812d94e5ac"}}