{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SHGO5FNNI62AS5HOQYZGIEQLP4","short_pith_number":"pith:SHGO5FNN","canonical_record":{"source":{"id":"1906.04024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-10T14:36:17Z","cross_cats_sorted":[],"title_canon_sha256":"565c66d844f05197c7e315b2fba12e762edb6467506b201769d19cd94ac65af2","abstract_canon_sha256":"7e94b591985e6462e997facdf76d024e733000bd4cbbb5af7241b00a6cdbbdf3"},"schema_version":"1.0"},"canonical_sha256":"91ccee95ad47b40974ee863264120b7f3ad774fc93f45e46b4593f8599ae4dc5","source":{"kind":"arxiv","id":"1906.04024","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.04024","created_at":"2026-05-17T23:43:44Z"},{"alias_kind":"arxiv_version","alias_value":"1906.04024v1","created_at":"2026-05-17T23:43:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04024","created_at":"2026-05-17T23:43:44Z"},{"alias_kind":"pith_short_12","alias_value":"SHGO5FNNI62A","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SHGO5FNNI62AS5HO","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SHGO5FNN","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SHGO5FNNI62AS5HOQYZGIEQLP4","target":"record","payload":{"canonical_record":{"source":{"id":"1906.04024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-10T14:36:17Z","cross_cats_sorted":[],"title_canon_sha256":"565c66d844f05197c7e315b2fba12e762edb6467506b201769d19cd94ac65af2","abstract_canon_sha256":"7e94b591985e6462e997facdf76d024e733000bd4cbbb5af7241b00a6cdbbdf3"},"schema_version":"1.0"},"canonical_sha256":"91ccee95ad47b40974ee863264120b7f3ad774fc93f45e46b4593f8599ae4dc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:44.135664Z","signature_b64":"z7SykdzBHxnZrxgXXbLN1Z6L2s0hfGBcbWsj/UgA/FufBoI6IAFMbvllln4qF/F2EN9GScJJffmGX/oqSaFABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91ccee95ad47b40974ee863264120b7f3ad774fc93f45e46b4593f8599ae4dc5","last_reissued_at":"2026-05-17T23:43:44.134943Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:44.134943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.04024","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":"2026-05-17T23:43:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DdwF9NpAyDI6qaM5OTJ2vuln/DseETJ9UilxPeOiJOQgVvGI+xnIxQhxLgiG1vWIWvOc7L2FzCTaftOzrGxnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T03:31:02.866187Z"},"content_sha256":"01191e6c6d7eeed41b39b3a4787f51e9b4a214d00e8fd6a041eae23a63cb0449","schema_version":"1.0","event_id":"sha256:01191e6c6d7eeed41b39b3a4787f51e9b4a214d00e8fd6a041eae23a63cb0449"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SHGO5FNNI62AS5HOQYZGIEQLP4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Odd Cycle Game and Connected Rules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adva Mond, Alexey Pokrovskiy, Christoph Spiegel, Jan Corsten, Tibor Szab\\'o","submitted_at":"2019-06-10T14:36:17Z","abstract_excerpt":"We study the positional game where two players, Maker and Breaker, alternately select respectively $1$ and $b$ previously unclaimed edges of $K_n$. Maker wins if she succeeds in claiming all edges of some odd cycle in $K_n$ and Breaker wins otherwise. Improving on a result of Bednarska and Pikhurko, we show that Maker wins the odd cycle game if $b \\leq ((4 - \\sqrt{6})/5 + o(1)) n$. We furthermore introduce \"connected rules\" and study the odd cycle game under them, both in the Maker-Breaker as well as in the Client-Waiter variant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04024","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":"2026-05-17T23:43:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dhSTAc1pjUfLKPKT8kQEhqGuodAyMjDn1sh+Yv/oPVjh4llvC1rj/b7ro5mbAMjAuT9M/w9VMglzkKgedTeQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T03:31:02.866557Z"},"content_sha256":"c640fd36a89679b5e40aa1ad9e76e389a506ad502debe2815da1e7d7291db1e2","schema_version":"1.0","event_id":"sha256:c640fd36a89679b5e40aa1ad9e76e389a506ad502debe2815da1e7d7291db1e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SHGO5FNNI62AS5HOQYZGIEQLP4/bundle.json","state_url":"https://pith.science/pith/SHGO5FNNI62AS5HOQYZGIEQLP4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SHGO5FNNI62AS5HOQYZGIEQLP4/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":"2026-05-21T03:31:02Z","links":{"resolver":"https://pith.science/pith/SHGO5FNNI62AS5HOQYZGIEQLP4","bundle":"https://pith.science/pith/SHGO5FNNI62AS5HOQYZGIEQLP4/bundle.json","state":"https://pith.science/pith/SHGO5FNNI62AS5HOQYZGIEQLP4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SHGO5FNNI62AS5HOQYZGIEQLP4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SHGO5FNNI62AS5HOQYZGIEQLP4","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":"7e94b591985e6462e997facdf76d024e733000bd4cbbb5af7241b00a6cdbbdf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-10T14:36:17Z","title_canon_sha256":"565c66d844f05197c7e315b2fba12e762edb6467506b201769d19cd94ac65af2"},"schema_version":"1.0","source":{"id":"1906.04024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.04024","created_at":"2026-05-17T23:43:44Z"},{"alias_kind":"arxiv_version","alias_value":"1906.04024v1","created_at":"2026-05-17T23:43:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04024","created_at":"2026-05-17T23:43:44Z"},{"alias_kind":"pith_short_12","alias_value":"SHGO5FNNI62A","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SHGO5FNNI62AS5HO","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SHGO5FNN","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:c640fd36a89679b5e40aa1ad9e76e389a506ad502debe2815da1e7d7291db1e2","target":"graph","created_at":"2026-05-17T23:43:44Z","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":"We study the positional game where two players, Maker and Breaker, alternately select respectively $1$ and $b$ previously unclaimed edges of $K_n$. Maker wins if she succeeds in claiming all edges of some odd cycle in $K_n$ and Breaker wins otherwise. Improving on a result of Bednarska and Pikhurko, we show that Maker wins the odd cycle game if $b \\leq ((4 - \\sqrt{6})/5 + o(1)) n$. We furthermore introduce \"connected rules\" and study the odd cycle game under them, both in the Maker-Breaker as well as in the Client-Waiter variant.","authors_text":"Adva Mond, Alexey Pokrovskiy, Christoph Spiegel, Jan Corsten, Tibor Szab\\'o","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-10T14:36:17Z","title":"On the Odd Cycle Game and Connected Rules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04024","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":"sha256:01191e6c6d7eeed41b39b3a4787f51e9b4a214d00e8fd6a041eae23a63cb0449","target":"record","created_at":"2026-05-17T23:43:44Z","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":"7e94b591985e6462e997facdf76d024e733000bd4cbbb5af7241b00a6cdbbdf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-10T14:36:17Z","title_canon_sha256":"565c66d844f05197c7e315b2fba12e762edb6467506b201769d19cd94ac65af2"},"schema_version":"1.0","source":{"id":"1906.04024","kind":"arxiv","version":1}},"canonical_sha256":"91ccee95ad47b40974ee863264120b7f3ad774fc93f45e46b4593f8599ae4dc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91ccee95ad47b40974ee863264120b7f3ad774fc93f45e46b4593f8599ae4dc5","first_computed_at":"2026-05-17T23:43:44.134943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:44.134943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z7SykdzBHxnZrxgXXbLN1Z6L2s0hfGBcbWsj/UgA/FufBoI6IAFMbvllln4qF/F2EN9GScJJffmGX/oqSaFABw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:44.135664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.04024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01191e6c6d7eeed41b39b3a4787f51e9b4a214d00e8fd6a041eae23a63cb0449","sha256:c640fd36a89679b5e40aa1ad9e76e389a506ad502debe2815da1e7d7291db1e2"],"state_sha256":"5a5557f85c42574e1d57869540bd420e0ab15a532d1f89b3da2dcf92b7a32469"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KYJsSCieyi/f+HPdWTFPOjL4pbQDmJYN/U//qgW8M4OJrtAADC9fa969iaQSJEx25fy9qGdtgZgtymCQat6nAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T03:31:02.868677Z","bundle_sha256":"10d1a32e0657a62eb7eccf386613d123dd962d015a6bb5f1da1c1b9cb59c33f8"}}