{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YCQGSN7K3GYY6Y35TCI7DPLIRW","short_pith_number":"pith:YCQGSN7K","canonical_record":{"source":{"id":"2607.18569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-07-20T23:04:55Z","cross_cats_sorted":[],"title_canon_sha256":"029f304c8e3922c64a60e17e2a5a578f297e3fe1145770c20a341770ba514616","abstract_canon_sha256":"75eb47f112f037e5beaa988c2e67bcdb1a93e037fe9750e990b1c63b7e984164"},"schema_version":"1.0"},"canonical_sha256":"c0a06937ead9b18f637d9891f1bd688d8c392400860140d6caf10120b89a99ab","source":{"kind":"arxiv","id":"2607.18569","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18569","created_at":"2026-07-22T00:22:54Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18569v1","created_at":"2026-07-22T00:22:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18569","created_at":"2026-07-22T00:22:54Z"},{"alias_kind":"pith_short_12","alias_value":"YCQGSN7K3GYY","created_at":"2026-07-22T00:22:54Z"},{"alias_kind":"pith_short_16","alias_value":"YCQGSN7K3GYY6Y35","created_at":"2026-07-22T00:22:54Z"},{"alias_kind":"pith_short_8","alias_value":"YCQGSN7K","created_at":"2026-07-22T00:22:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YCQGSN7K3GYY6Y35TCI7DPLIRW","target":"record","payload":{"canonical_record":{"source":{"id":"2607.18569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-07-20T23:04:55Z","cross_cats_sorted":[],"title_canon_sha256":"029f304c8e3922c64a60e17e2a5a578f297e3fe1145770c20a341770ba514616","abstract_canon_sha256":"75eb47f112f037e5beaa988c2e67bcdb1a93e037fe9750e990b1c63b7e984164"},"schema_version":"1.0"},"canonical_sha256":"c0a06937ead9b18f637d9891f1bd688d8c392400860140d6caf10120b89a99ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T00:22:54.721104Z","signature_b64":"WcmKZCkYdSJswkOOfw22ntW0dbuTLrpoQpA+cKOe0cP9cTSZuj6XoKmbZoZuPeshMJdYTdn/eWfKdnLY3hxtDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0a06937ead9b18f637d9891f1bd688d8c392400860140d6caf10120b89a99ab","last_reissued_at":"2026-07-22T00:22:54.720360Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T00:22:54.720360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.18569","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":"2026-07-22T00:22:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4GzRLXDEzAJKl7ufEffB+3VL3FeRlZynXoDkznt2JittsBYMrQpoyboU92yCf5p81TZkhI/2vfavgrLaaRFzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T21:37:36.806989Z"},"content_sha256":"ed2fba8dc136dddd64bb43214c84eb7ce615b4c0f76ae791203b3c5e3388e5e1","schema_version":"1.0","event_id":"sha256:ed2fba8dc136dddd64bb43214c84eb7ce615b4c0f76ae791203b3c5e3388e5e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YCQGSN7K3GYY6Y35TCI7DPLIRW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anand Srivastav, Julian Christoph Brinkmann","submitted_at":"2026-07-20T23:04:55Z","abstract_excerpt":"In this paper, we present new polynomial-time algorithms for determining the winner of the unbiased triangle game played on the edge set of general graphs. To that end, we propose to view the game through the edge-triangle incidence graph instead of the standard hypergraph model. We identify a necessary and sufficient winning condition for Maker in terms of the edge-triangle incidence graph and show that winning strategies achieving this condition as fast as possible play monotonically in the sense that they only consider monotonically decreasing connected subgraphs of the edge-triangle incide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18569","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/2607.18569/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":"2026-07-22T00:22:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+KHS8CTXmzLwm9wQhmMHGe69/YezrHlnsRnv5lW2/b8CfYOXgCkPQRMtA+ViU03AjDJIAYCrJpYNYqmFVgoLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T21:37:36.807490Z"},"content_sha256":"295fd138a1a2ee3834082dada451f018a0ae3865aea3b7bb731426e2aad076b1","schema_version":"1.0","event_id":"sha256:295fd138a1a2ee3834082dada451f018a0ae3865aea3b7bb731426e2aad076b1"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:YCQGSN7K3GYY6Y35TCI7DPLIRW","target":"integrity","payload":{"note":"DOI is split by whitespace or line breaks in the printed bibliography. Reconstructed DOI 10.1016/J.DAM.2024.11.012 resolves to 'Complexity of Maker–Breaker games on edge sets of graphs'. A reader following the printed text alone cannot reach it.","snippet":"Éric Duchêne, Valentin Gledel, Fionn Mc Inerney, Nicolas Nisse, Nacim Oijid, Aline Parreau, and Milos Stojakovic. Complexity of Maker-Breaker games on edge sets of graphs.Discret. Appl. Math., 361:502–522, 2025.doi:10.1016/J.DAM. 2024.11.012","arxiv_id":"2607.18569","detector":"doi_compliance","evidence":{"ref_index":9,"verdict_class":"incontrovertible","resolved_title":"Complexity of Maker–Breaker games on edge sets of graphs","printed_excerpt":"10.1016/j.dam","reconstructed_doi":"10.1016/J.DAM.2024.11.012"},"severity":"advisory","ref_index":9,"audited_at":"2026-08-01T15:19:02.074760Z","event_type":"pith.integrity.v1","detected_doi":"10.1016/J.DAM.2024.11.012","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"f433aba105c5a0a10f8ba9a669836f3b35c68e10d764ce631a32137e2086a336","paper_version":1,"verdict_class":"incontrovertible","resolved_title":"Complexity of Maker–Breaker games on edge sets of graphs","detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":16041,"payload_sha256":"e7724a77e2f9ea056c145604f59554b3b846b9edefe89a0e76a3b828dd00f66e","signature_b64":"M8558ysF9V5xxFp+o9nuMOJ2HICE8sk0qs5s3oA/ls2AbSebs0J306IHytjaQwEp7JnH1ZRKlhVnkWni+HBrBw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-01T15:23:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0qlg1p1gBdAixlkEx09PybUemADsT0SpW+lCrz/2rh/prn17C7JV+g93vokeBHDSS0NAnJeSG19CMCWRTdcsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T21:37:36.811468Z"},"content_sha256":"25b7929ccf56754bafa74cec013e06af980e3d0648224ce0cc7695e28d75bfb8","schema_version":"1.0","event_id":"sha256:25b7929ccf56754bafa74cec013e06af980e3d0648224ce0cc7695e28d75bfb8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCQGSN7K3GYY6Y35TCI7DPLIRW/bundle.json","state_url":"https://pith.science/pith/YCQGSN7K3GYY6Y35TCI7DPLIRW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCQGSN7K3GYY6Y35TCI7DPLIRW/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":"2026-08-21T21:37:36Z","links":{"resolver":"https://pith.science/pith/YCQGSN7K3GYY6Y35TCI7DPLIRW","bundle":"https://pith.science/pith/YCQGSN7K3GYY6Y35TCI7DPLIRW/bundle.json","state":"https://pith.science/pith/YCQGSN7K3GYY6Y35TCI7DPLIRW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCQGSN7K3GYY6Y35TCI7DPLIRW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YCQGSN7K3GYY6Y35TCI7DPLIRW","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"75eb47f112f037e5beaa988c2e67bcdb1a93e037fe9750e990b1c63b7e984164","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-07-20T23:04:55Z","title_canon_sha256":"029f304c8e3922c64a60e17e2a5a578f297e3fe1145770c20a341770ba514616"},"schema_version":"1.0","source":{"id":"2607.18569","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18569","created_at":"2026-07-22T00:22:54Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18569v1","created_at":"2026-07-22T00:22:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18569","created_at":"2026-07-22T00:22:54Z"},{"alias_kind":"pith_short_12","alias_value":"YCQGSN7K3GYY","created_at":"2026-07-22T00:22:54Z"},{"alias_kind":"pith_short_16","alias_value":"YCQGSN7K3GYY6Y35","created_at":"2026-07-22T00:22:54Z"},{"alias_kind":"pith_short_8","alias_value":"YCQGSN7K","created_at":"2026-07-22T00:22:54Z"}],"graph_snapshots":[{"event_id":"sha256:295fd138a1a2ee3834082dada451f018a0ae3865aea3b7bb731426e2aad076b1","target":"graph","created_at":"2026-07-22T00:22:54Z","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/2607.18569/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present new polynomial-time algorithms for determining the winner of the unbiased triangle game played on the edge set of general graphs. To that end, we propose to view the game through the edge-triangle incidence graph instead of the standard hypergraph model. We identify a necessary and sufficient winning condition for Maker in terms of the edge-triangle incidence graph and show that winning strategies achieving this condition as fast as possible play monotonically in the sense that they only consider monotonically decreasing connected subgraphs of the edge-triangle incide","authors_text":"Anand Srivastav, Julian Christoph Brinkmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-07-20T23:04:55Z","title":"Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18569","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:ed2fba8dc136dddd64bb43214c84eb7ce615b4c0f76ae791203b3c5e3388e5e1","target":"record","created_at":"2026-07-22T00:22:54Z","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":"75eb47f112f037e5beaa988c2e67bcdb1a93e037fe9750e990b1c63b7e984164","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-07-20T23:04:55Z","title_canon_sha256":"029f304c8e3922c64a60e17e2a5a578f297e3fe1145770c20a341770ba514616"},"schema_version":"1.0","source":{"id":"2607.18569","kind":"arxiv","version":1}},"canonical_sha256":"c0a06937ead9b18f637d9891f1bd688d8c392400860140d6caf10120b89a99ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0a06937ead9b18f637d9891f1bd688d8c392400860140d6caf10120b89a99ab","first_computed_at":"2026-07-22T00:22:54.720360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T00:22:54.720360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WcmKZCkYdSJswkOOfw22ntW0dbuTLrpoQpA+cKOe0cP9cTSZuj6XoKmbZoZuPeshMJdYTdn/eWfKdnLY3hxtDQ==","signature_status":"signed_v1","signed_at":"2026-07-22T00:22:54.721104Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18569","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed2fba8dc136dddd64bb43214c84eb7ce615b4c0f76ae791203b3c5e3388e5e1","sha256:295fd138a1a2ee3834082dada451f018a0ae3865aea3b7bb731426e2aad076b1","sha256:25b7929ccf56754bafa74cec013e06af980e3d0648224ce0cc7695e28d75bfb8"],"state_sha256":"71b438aad24ba204a40f57fa91f30f050ac301381f1ceb65c1bc47667cb8bf5e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6sQap7u8BoU756U+Xd5qBxXwn+IYaNExmoFoX0qI/J5NZk5qWOiQkUrzla0JDIyr+KyRLDVpIGunOb5IC1mBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T21:37:36.813765Z","bundle_sha256":"1eaff616218d199de094ffbe7d9bd286f7bc7f263d2c5de23421ba4505b371d6"}}