{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GYAPQ2PZCTHGZV4KRPIK5RQIKH","short_pith_number":"pith:GYAPQ2PZ","canonical_record":{"source":{"id":"2605.24845","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2026-05-24T03:29:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"912b2e610492d8130fc6ec46fa54f7cb2269aea0ba4f189caa16f121570064bf","abstract_canon_sha256":"af2a7c48fc45de834ac6a718af96b8f5691b13b035ff1f1ff807f16687cd121c"},"schema_version":"1.0"},"canonical_sha256":"3600f869f914ce6cd78a8bd0aec60851dbb1316a974248be358583f671dd2171","source":{"kind":"arxiv","id":"2605.24845","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24845","created_at":"2026-05-26T01:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24845v1","created_at":"2026-05-26T01:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24845","created_at":"2026-05-26T01:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"GYAPQ2PZCTHG","created_at":"2026-05-26T01:04:01Z"},{"alias_kind":"pith_short_16","alias_value":"GYAPQ2PZCTHGZV4K","created_at":"2026-05-26T01:04:01Z"},{"alias_kind":"pith_short_8","alias_value":"GYAPQ2PZ","created_at":"2026-05-26T01:04:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GYAPQ2PZCTHGZV4KRPIK5RQIKH","target":"record","payload":{"canonical_record":{"source":{"id":"2605.24845","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2026-05-24T03:29:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"912b2e610492d8130fc6ec46fa54f7cb2269aea0ba4f189caa16f121570064bf","abstract_canon_sha256":"af2a7c48fc45de834ac6a718af96b8f5691b13b035ff1f1ff807f16687cd121c"},"schema_version":"1.0"},"canonical_sha256":"3600f869f914ce6cd78a8bd0aec60851dbb1316a974248be358583f671dd2171","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:04:01.454810Z","signature_b64":"oEQ8Rwz/8ir/bgytKFES659YZ6o1Hc5kMNlS++Ij1zUoNnrft2onuUto7n2u/8jMwn9nBunyQY/v6BMw5pbhAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3600f869f914ce6cd78a8bd0aec60851dbb1316a974248be358583f671dd2171","last_reissued_at":"2026-05-26T01:04:01.453996Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:04:01.453996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.24845","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":"2026-05-26T01:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WDevN3VD7KyDHOHXZ6//zXjOefggFNpQKY8w08yTqdPMZnn+sv6GeKHOUO7U5FMQUjYyWARuxH24727hMTWRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:38:52.774538Z"},"content_sha256":"77740cd77c19a93ab48408bf70634ec942b543c117e7a80ede45ec5f1d2ba80e","schema_version":"1.0","event_id":"sha256:77740cd77c19a93ab48408bf70634ec942b543c117e7a80ede45ec5f1d2ba80e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GYAPQ2PZCTHGZV4KRPIK5RQIKH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving Combinatorial Counting Problems with Weighted First-Order Model Counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.AI","authors_text":"Juhua Pu, Ond\\v{r}ej Ku\\v{z}elka, Yuanhong Wang, Yuxu Zhou, Yuyi Wang","submitted_at":"2026-05-24T03:29:19Z","abstract_excerpt":"Combinatorial counting problems pervade artificial intelligence, statistics, and discrete mathematics. Whether the task is enumerating subsets, multisets, permutations, partitions, or compositions under structural and arithmetic constraints, solving it remains a stubbornly manual exercise. Closed-form derivations are powerful but brittle, while naive encodings to propositional model counting or constraint satisfaction destroy the exchangeability that makes counting tractable in the first place. We present Cofola (COmbinatorial counting LAnguage with First-Order logic), a typed declarative lang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24845","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/2605.24845/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":"2026-05-26T01:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EYga4XR6HJVc6IHCwY2Ruk5TRiSa6HeHOeIKagB5PMuA/XPbbnxdaOjyvVQq83z0d9+YCcoFxLst5PzwqLJDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:38:52.774914Z"},"content_sha256":"58fda32d62211405de779820d9a1d5b98ffcb2510c6c7ab5cbc4f8775ef7383b","schema_version":"1.0","event_id":"sha256:58fda32d62211405de779820d9a1d5b98ffcb2510c6c7ab5cbc4f8775ef7383b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GYAPQ2PZCTHGZV4KRPIK5RQIKH/bundle.json","state_url":"https://pith.science/pith/GYAPQ2PZCTHGZV4KRPIK5RQIKH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GYAPQ2PZCTHGZV4KRPIK5RQIKH/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":"2026-07-02T12:38:52Z","links":{"resolver":"https://pith.science/pith/GYAPQ2PZCTHGZV4KRPIK5RQIKH","bundle":"https://pith.science/pith/GYAPQ2PZCTHGZV4KRPIK5RQIKH/bundle.json","state":"https://pith.science/pith/GYAPQ2PZCTHGZV4KRPIK5RQIKH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GYAPQ2PZCTHGZV4KRPIK5RQIKH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GYAPQ2PZCTHGZV4KRPIK5RQIKH","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":"af2a7c48fc45de834ac6a718af96b8f5691b13b035ff1f1ff807f16687cd121c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2026-05-24T03:29:19Z","title_canon_sha256":"912b2e610492d8130fc6ec46fa54f7cb2269aea0ba4f189caa16f121570064bf"},"schema_version":"1.0","source":{"id":"2605.24845","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24845","created_at":"2026-05-26T01:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24845v1","created_at":"2026-05-26T01:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24845","created_at":"2026-05-26T01:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"GYAPQ2PZCTHG","created_at":"2026-05-26T01:04:01Z"},{"alias_kind":"pith_short_16","alias_value":"GYAPQ2PZCTHGZV4K","created_at":"2026-05-26T01:04:01Z"},{"alias_kind":"pith_short_8","alias_value":"GYAPQ2PZ","created_at":"2026-05-26T01:04:01Z"}],"graph_snapshots":[{"event_id":"sha256:58fda32d62211405de779820d9a1d5b98ffcb2510c6c7ab5cbc4f8775ef7383b","target":"graph","created_at":"2026-05-26T01:04:01Z","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/2605.24845/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Combinatorial counting problems pervade artificial intelligence, statistics, and discrete mathematics. Whether the task is enumerating subsets, multisets, permutations, partitions, or compositions under structural and arithmetic constraints, solving it remains a stubbornly manual exercise. Closed-form derivations are powerful but brittle, while naive encodings to propositional model counting or constraint satisfaction destroy the exchangeability that makes counting tractable in the first place. We present Cofola (COmbinatorial counting LAnguage with First-Order logic), a typed declarative lang","authors_text":"Juhua Pu, Ond\\v{r}ej Ku\\v{z}elka, Yuanhong Wang, Yuxu Zhou, Yuyi Wang","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2026-05-24T03:29:19Z","title":"Solving Combinatorial Counting Problems with Weighted First-Order Model Counting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24845","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":"sha256:77740cd77c19a93ab48408bf70634ec942b543c117e7a80ede45ec5f1d2ba80e","target":"record","created_at":"2026-05-26T01:04:01Z","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":"af2a7c48fc45de834ac6a718af96b8f5691b13b035ff1f1ff807f16687cd121c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2026-05-24T03:29:19Z","title_canon_sha256":"912b2e610492d8130fc6ec46fa54f7cb2269aea0ba4f189caa16f121570064bf"},"schema_version":"1.0","source":{"id":"2605.24845","kind":"arxiv","version":1}},"canonical_sha256":"3600f869f914ce6cd78a8bd0aec60851dbb1316a974248be358583f671dd2171","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3600f869f914ce6cd78a8bd0aec60851dbb1316a974248be358583f671dd2171","first_computed_at":"2026-05-26T01:04:01.453996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:04:01.453996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oEQ8Rwz/8ir/bgytKFES659YZ6o1Hc5kMNlS++Ij1zUoNnrft2onuUto7n2u/8jMwn9nBunyQY/v6BMw5pbhAA==","signature_status":"signed_v1","signed_at":"2026-05-26T01:04:01.454810Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.24845","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77740cd77c19a93ab48408bf70634ec942b543c117e7a80ede45ec5f1d2ba80e","sha256:58fda32d62211405de779820d9a1d5b98ffcb2510c6c7ab5cbc4f8775ef7383b"],"state_sha256":"408e8a78d6c5d1e708d246eacdc7969346e57a599b493687c3e9c39c63f04ed9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pLiR4dPdCOJPVI1Iy21FvzRikZ4cdjey3QXFnFbR7R8+sHSDBrI6YzIkKPcbxLrqAvS8Hc8OOSWPJ0AJ6iCzDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T12:38:52.777143Z","bundle_sha256":"98828526c3c066ad5a903e9bc8fcb9412effa7239887c26c49cc7117bc36ccdf"}}