{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:UXX2KT6S6MHBLUCLDNOCOXAUQ2","short_pith_number":"pith:UXX2KT6S","canonical_record":{"source":{"id":"2511.04258","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-11-06T10:49:07Z","cross_cats_sorted":[],"title_canon_sha256":"e2ba3b61729dbff14bdb726cf2b2c94c1266227a258baf71fc206000f850b370","abstract_canon_sha256":"2077e806a494f73b29d6d1950cba3f4664bd45f9511d3398bf40b9b521855abb"},"schema_version":"1.0"},"canonical_sha256":"a5efa54fd2f30e15d04b1b5c275c1486a660bb12078e8e183166bb8bca4de7c0","source":{"kind":"arxiv","id":"2511.04258","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.04258","created_at":"2026-07-01T01:17:42Z"},{"alias_kind":"arxiv_version","alias_value":"2511.04258v2","created_at":"2026-07-01T01:17:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.04258","created_at":"2026-07-01T01:17:42Z"},{"alias_kind":"pith_short_12","alias_value":"UXX2KT6S6MHB","created_at":"2026-07-01T01:17:42Z"},{"alias_kind":"pith_short_16","alias_value":"UXX2KT6S6MHBLUCL","created_at":"2026-07-01T01:17:42Z"},{"alias_kind":"pith_short_8","alias_value":"UXX2KT6S","created_at":"2026-07-01T01:17:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:UXX2KT6S6MHBLUCLDNOCOXAUQ2","target":"record","payload":{"canonical_record":{"source":{"id":"2511.04258","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-11-06T10:49:07Z","cross_cats_sorted":[],"title_canon_sha256":"e2ba3b61729dbff14bdb726cf2b2c94c1266227a258baf71fc206000f850b370","abstract_canon_sha256":"2077e806a494f73b29d6d1950cba3f4664bd45f9511d3398bf40b9b521855abb"},"schema_version":"1.0"},"canonical_sha256":"a5efa54fd2f30e15d04b1b5c275c1486a660bb12078e8e183166bb8bca4de7c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:17:42.813451Z","signature_b64":"D8+ld6/3lPZlCyvTa6d/fVSrLAECuCAnTLA85mFdpOC/E7giF0twQzgFzngro84VEV+Rp05tADIMQyYhx6ezDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5efa54fd2f30e15d04b1b5c275c1486a660bb12078e8e183166bb8bca4de7c0","last_reissued_at":"2026-07-01T01:17:42.812817Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:17:42.812817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2511.04258","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-01T01:17:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YaywYTgi6jsd0KIA4G9ObBfyU6lhBFBtsUnR8PIu7nr4pag/i8AZ9GkIRH0E7kW/MP/8EVSGcsyMD3b7/Nl5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T08:39:23.440664Z"},"content_sha256":"cfa27d4dbd37925c5bc9028257ca9d5a8997ddb1757e0ee089cb9a0ed0a67b62","schema_version":"1.0","event_id":"sha256:cfa27d4dbd37925c5bc9028257ca9d5a8997ddb1757e0ee089cb9a0ed0a67b62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:UXX2KT6S6MHBLUCLDNOCOXAUQ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting Patterns in Degenerate Graphs in Constant Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Akash Pareek, Anant Kumar, Balagopal Komarath","submitted_at":"2025-11-06T10:49:07Z","abstract_excerpt":"For a fixed pattern graph, we study the algorithmic complexity of counting homomorphisms, subgraph isomorphisms, and induced subgraph isomorphisms into an $n$-vertex, $d$-degenerate host graph. Bressan (Algorithmica, 2021) introduced the notion of DAG treewidth and showed that counting homomorphisms and induced subgraphs can be performed efficiently using dynamic programming that requires polynomial space. In this work, we introduce a new graph parameter, called DAG treedepth, which enables efficient divide-and-conquer algorithms for counting homomorphisms in $d$-degenerate host graphs using o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.04258","kind":"arxiv","version":2},"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/2511.04258/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":"2026-07-01T01:17:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"syb51VuxTsPp3kYJgdiZHYn3WlPkVHFvdwsEUQ7dBSvZ9C4JG6auo0vlo4i3oqqe2zlbFe6B8Ei5k/iroOT7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T08:39:23.441162Z"},"content_sha256":"703c3195f9c605f0a6c174ddce6e8620479e60041d406e0000eec0608446c9ec","schema_version":"1.0","event_id":"sha256:703c3195f9c605f0a6c174ddce6e8620479e60041d406e0000eec0608446c9ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXX2KT6S6MHBLUCLDNOCOXAUQ2/bundle.json","state_url":"https://pith.science/pith/UXX2KT6S6MHBLUCLDNOCOXAUQ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXX2KT6S6MHBLUCLDNOCOXAUQ2/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":"2026-08-12T08:39:23Z","links":{"resolver":"https://pith.science/pith/UXX2KT6S6MHBLUCLDNOCOXAUQ2","bundle":"https://pith.science/pith/UXX2KT6S6MHBLUCLDNOCOXAUQ2/bundle.json","state":"https://pith.science/pith/UXX2KT6S6MHBLUCLDNOCOXAUQ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXX2KT6S6MHBLUCLDNOCOXAUQ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UXX2KT6S6MHBLUCLDNOCOXAUQ2","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":"2077e806a494f73b29d6d1950cba3f4664bd45f9511d3398bf40b9b521855abb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-11-06T10:49:07Z","title_canon_sha256":"e2ba3b61729dbff14bdb726cf2b2c94c1266227a258baf71fc206000f850b370"},"schema_version":"1.0","source":{"id":"2511.04258","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.04258","created_at":"2026-07-01T01:17:42Z"},{"alias_kind":"arxiv_version","alias_value":"2511.04258v2","created_at":"2026-07-01T01:17:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.04258","created_at":"2026-07-01T01:17:42Z"},{"alias_kind":"pith_short_12","alias_value":"UXX2KT6S6MHB","created_at":"2026-07-01T01:17:42Z"},{"alias_kind":"pith_short_16","alias_value":"UXX2KT6S6MHBLUCL","created_at":"2026-07-01T01:17:42Z"},{"alias_kind":"pith_short_8","alias_value":"UXX2KT6S","created_at":"2026-07-01T01:17:42Z"}],"graph_snapshots":[{"event_id":"sha256:703c3195f9c605f0a6c174ddce6e8620479e60041d406e0000eec0608446c9ec","target":"graph","created_at":"2026-07-01T01:17:42Z","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/2511.04258/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a fixed pattern graph, we study the algorithmic complexity of counting homomorphisms, subgraph isomorphisms, and induced subgraph isomorphisms into an $n$-vertex, $d$-degenerate host graph. Bressan (Algorithmica, 2021) introduced the notion of DAG treewidth and showed that counting homomorphisms and induced subgraphs can be performed efficiently using dynamic programming that requires polynomial space. In this work, we introduce a new graph parameter, called DAG treedepth, which enables efficient divide-and-conquer algorithms for counting homomorphisms in $d$-degenerate host graphs using o","authors_text":"Akash Pareek, Anant Kumar, Balagopal Komarath","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-11-06T10:49:07Z","title":"Counting Patterns in Degenerate Graphs in Constant Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.04258","kind":"arxiv","version":2},"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:cfa27d4dbd37925c5bc9028257ca9d5a8997ddb1757e0ee089cb9a0ed0a67b62","target":"record","created_at":"2026-07-01T01:17:42Z","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":"2077e806a494f73b29d6d1950cba3f4664bd45f9511d3398bf40b9b521855abb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-11-06T10:49:07Z","title_canon_sha256":"e2ba3b61729dbff14bdb726cf2b2c94c1266227a258baf71fc206000f850b370"},"schema_version":"1.0","source":{"id":"2511.04258","kind":"arxiv","version":2}},"canonical_sha256":"a5efa54fd2f30e15d04b1b5c275c1486a660bb12078e8e183166bb8bca4de7c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5efa54fd2f30e15d04b1b5c275c1486a660bb12078e8e183166bb8bca4de7c0","first_computed_at":"2026-07-01T01:17:42.812817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:17:42.812817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D8+ld6/3lPZlCyvTa6d/fVSrLAECuCAnTLA85mFdpOC/E7giF0twQzgFzngro84VEV+Rp05tADIMQyYhx6ezDA==","signature_status":"signed_v1","signed_at":"2026-07-01T01:17:42.813451Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.04258","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfa27d4dbd37925c5bc9028257ca9d5a8997ddb1757e0ee089cb9a0ed0a67b62","sha256:703c3195f9c605f0a6c174ddce6e8620479e60041d406e0000eec0608446c9ec"],"state_sha256":"a03e274e05ee617c8f82ef509e58f4d62c2de92618354a19c6be85052c987e63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wMD+AUIPapYtC/kjAERLRa4MoyROPuntVlIk7ZKTvm1YpiB+MIidzpFRRkt/hyYuYL62DQ6NtBHcVmn+1W4uCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T08:39:23.446623Z","bundle_sha256":"84384062a9922d630f8f4a7bd6bac6f172d12a32c6c227928ab81bc481b5dc09"}}