{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:R2WZWFGPDESR3QH6CFGEZFV4GC","short_pith_number":"pith:R2WZWFGP","canonical_record":{"source":{"id":"1609.06057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-20T08:51:02Z","cross_cats_sorted":[],"title_canon_sha256":"f82d7601b03ea2696f26bcc4271d2e05e1f49926f3015c35b578e36f1102620d","abstract_canon_sha256":"c4cf67139830586a1acc9a1c9bb4f276c919311fa4e0fd571cb5e1c3e5700e43"},"schema_version":"1.0"},"canonical_sha256":"8ead9b14cf19251dc0fe114c4c96bc309be4b30f33caca80ac0a0c40f5043a37","source":{"kind":"arxiv","id":"1609.06057","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06057","created_at":"2026-05-18T01:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06057v1","created_at":"2026-05-18T01:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06057","created_at":"2026-05-18T01:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"R2WZWFGPDESR","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R2WZWFGPDESR3QH6","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R2WZWFGP","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:R2WZWFGPDESR3QH6CFGEZFV4GC","target":"record","payload":{"canonical_record":{"source":{"id":"1609.06057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-20T08:51:02Z","cross_cats_sorted":[],"title_canon_sha256":"f82d7601b03ea2696f26bcc4271d2e05e1f49926f3015c35b578e36f1102620d","abstract_canon_sha256":"c4cf67139830586a1acc9a1c9bb4f276c919311fa4e0fd571cb5e1c3e5700e43"},"schema_version":"1.0"},"canonical_sha256":"8ead9b14cf19251dc0fe114c4c96bc309be4b30f33caca80ac0a0c40f5043a37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:16.808649Z","signature_b64":"6xSwXG+YoNiZWsWyJL+EPDnYFcDeKJeKIAdnV0LrETKs6ifFPLBvtKuQWxfqp0rmJU6DiTTz5jLHgiwN67DTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ead9b14cf19251dc0fe114c4c96bc309be4b30f33caca80ac0a0c40f5043a37","last_reissued_at":"2026-05-18T01:04:16.808237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:16.808237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.06057","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":"2026-05-18T01:04:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hH42GKStcNwzIfjfD4IXdX3IdDL4eq5yC1ps2CNW+9h8TwH5Zzpb/cCltzyZtFovcxMtPtt7UHx2Yl5ZuYbzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:27:18.486669Z"},"content_sha256":"6101a0083d47b44777dc557ee5890205e255224953d1ff1ba126edf7760f8f22","schema_version":"1.0","event_id":"sha256:6101a0083d47b44777dc557ee5890205e255224953d1ff1ba126edf7760f8f22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:R2WZWFGPDESR3QH6CFGEZFV4GC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abelian Ramsey Length and Asymptotic Lower Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vincent Jug\\'e","submitted_at":"2016-09-20T08:51:02Z","abstract_excerpt":"This technical note aims at evaluating an asymptotic lower bound on abelian Ramsey lengths."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06057","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":"2026-05-18T01:04:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3GH8poP8SHNuhAKbN0xJYRj7GfzmOOQZJMKCogHbJaGLxd5AvEvnEHTGSqndsqR8Z/VY0D6CRqskVp1szLbmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:27:18.487021Z"},"content_sha256":"05449f7c7e5c702af65a94e795097365b5dd111e37cbd2294d0f91e4d4a3dec4","schema_version":"1.0","event_id":"sha256:05449f7c7e5c702af65a94e795097365b5dd111e37cbd2294d0f91e4d4a3dec4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R2WZWFGPDESR3QH6CFGEZFV4GC/bundle.json","state_url":"https://pith.science/pith/R2WZWFGPDESR3QH6CFGEZFV4GC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R2WZWFGPDESR3QH6CFGEZFV4GC/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":"2026-06-02T20:27:18Z","links":{"resolver":"https://pith.science/pith/R2WZWFGPDESR3QH6CFGEZFV4GC","bundle":"https://pith.science/pith/R2WZWFGPDESR3QH6CFGEZFV4GC/bundle.json","state":"https://pith.science/pith/R2WZWFGPDESR3QH6CFGEZFV4GC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R2WZWFGPDESR3QH6CFGEZFV4GC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:R2WZWFGPDESR3QH6CFGEZFV4GC","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":"c4cf67139830586a1acc9a1c9bb4f276c919311fa4e0fd571cb5e1c3e5700e43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-20T08:51:02Z","title_canon_sha256":"f82d7601b03ea2696f26bcc4271d2e05e1f49926f3015c35b578e36f1102620d"},"schema_version":"1.0","source":{"id":"1609.06057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06057","created_at":"2026-05-18T01:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06057v1","created_at":"2026-05-18T01:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06057","created_at":"2026-05-18T01:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"R2WZWFGPDESR","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R2WZWFGPDESR3QH6","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R2WZWFGP","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:05449f7c7e5c702af65a94e795097365b5dd111e37cbd2294d0f91e4d4a3dec4","target":"graph","created_at":"2026-05-18T01:04:16Z","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":"This technical note aims at evaluating an asymptotic lower bound on abelian Ramsey lengths.","authors_text":"Vincent Jug\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-20T08:51:02Z","title":"Abelian Ramsey Length and Asymptotic Lower Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06057","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":"sha256:6101a0083d47b44777dc557ee5890205e255224953d1ff1ba126edf7760f8f22","target":"record","created_at":"2026-05-18T01:04:16Z","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":"c4cf67139830586a1acc9a1c9bb4f276c919311fa4e0fd571cb5e1c3e5700e43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-20T08:51:02Z","title_canon_sha256":"f82d7601b03ea2696f26bcc4271d2e05e1f49926f3015c35b578e36f1102620d"},"schema_version":"1.0","source":{"id":"1609.06057","kind":"arxiv","version":1}},"canonical_sha256":"8ead9b14cf19251dc0fe114c4c96bc309be4b30f33caca80ac0a0c40f5043a37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ead9b14cf19251dc0fe114c4c96bc309be4b30f33caca80ac0a0c40f5043a37","first_computed_at":"2026-05-18T01:04:16.808237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:16.808237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6xSwXG+YoNiZWsWyJL+EPDnYFcDeKJeKIAdnV0LrETKs6ifFPLBvtKuQWxfqp0rmJU6DiTTz5jLHgiwN67DTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:16.808649Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6101a0083d47b44777dc557ee5890205e255224953d1ff1ba126edf7760f8f22","sha256:05449f7c7e5c702af65a94e795097365b5dd111e37cbd2294d0f91e4d4a3dec4"],"state_sha256":"7c0851585fcf05c8c71578ea7ce30d9629874bed816519ec9ca08ea2ae42e3a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IIg0fLi7R5TbRTp7eR1DSY08aVwSS/hzfMxUtr4PuDou7XWU5NFGsY45vRXkzhnO3DyBgW/qMIsv4LMl+t2KDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:27:18.489429Z","bundle_sha256":"4d5fa063f07c8b8fd656d4f72f4f5c75baf1f537c7ddc0b4775832638b1cc073"}}