{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BPJ6WDJECAMNWOTBK2RYIQQWHY","short_pith_number":"pith:BPJ6WDJE","canonical_record":{"source":{"id":"2502.04311","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-06T18:54:00Z","cross_cats_sorted":[],"title_canon_sha256":"f2c9365275e28da17a1efd06bd18b105ccbf5c2dbd44ee283ecfddfc68898c47","abstract_canon_sha256":"c2397a344cda0b58e04026c004365de3835d5ed81ba85b1a524f8bd799cb8ba7"},"schema_version":"1.0"},"canonical_sha256":"0bd3eb0d241018db3a6156a38442163e011a12fa147a84b7b3e6b7fa3deed9d3","source":{"kind":"arxiv","id":"2502.04311","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.04311","created_at":"2026-07-05T10:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"2502.04311v1","created_at":"2026-07-05T10:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.04311","created_at":"2026-07-05T10:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"BPJ6WDJECAMN","created_at":"2026-07-05T10:10:36Z"},{"alias_kind":"pith_short_16","alias_value":"BPJ6WDJECAMNWOTB","created_at":"2026-07-05T10:10:36Z"},{"alias_kind":"pith_short_8","alias_value":"BPJ6WDJE","created_at":"2026-07-05T10:10:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BPJ6WDJECAMNWOTBK2RYIQQWHY","target":"record","payload":{"canonical_record":{"source":{"id":"2502.04311","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-06T18:54:00Z","cross_cats_sorted":[],"title_canon_sha256":"f2c9365275e28da17a1efd06bd18b105ccbf5c2dbd44ee283ecfddfc68898c47","abstract_canon_sha256":"c2397a344cda0b58e04026c004365de3835d5ed81ba85b1a524f8bd799cb8ba7"},"schema_version":"1.0"},"canonical_sha256":"0bd3eb0d241018db3a6156a38442163e011a12fa147a84b7b3e6b7fa3deed9d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:10:36.630027Z","signature_b64":"XEG7IWqrMISMqMiS3ggs+KyTS8l/p6xEIYF0oRn7Stb4UM0cZnDqqey6kwvhCDPa81q5XrteK/SJJH0WjLP9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bd3eb0d241018db3a6156a38442163e011a12fa147a84b7b3e6b7fa3deed9d3","last_reissued_at":"2026-07-05T10:10:36.629571Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:10:36.629571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.04311","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":"2026-07-05T10:10:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wnd2opzXO7H4pWXxvIl/WBEYOTLpV1uW6Bfw2X3w+MoLqPElizE2BaZEM9AlP8iI1dSx4qrLZ+PPJX8DnUwIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:17:51.596738Z"},"content_sha256":"f95c7efe471e4b57a5f8c30f185c784f6334692bc33b6357fef52cddbbf6ae20","schema_version":"1.0","event_id":"sha256:f95c7efe471e4b57a5f8c30f185c784f6334692bc33b6357fef52cddbbf6ae20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BPJ6WDJECAMNWOTBK2RYIQQWHY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ramsey-Theoretic Characterizations of Classically Non-Ramseyian Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bryce Alan Christopherson","submitted_at":"2025-02-06T18:54:00Z","abstract_excerpt":"In this paper, we will develop a significantly more general notion of classical Ramsey numbers (extending most other graph-theoretic generalizations) and make some preliminary characterizations of these new Ramsey numbers using simple algebraic tools. Throughout, we make a case arguing that, while our access to specific values of Ramsey numbers (or, in general, precise numerical solutions to Ramsey-theoretic problems) may be limited, the interplay between and overall structure of Ramseyian objects is likely tractable. To support the relevancy of this perspective, we conclude by demonstrating t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04311","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/2502.04311/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":"2026-07-05T10:10:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1KYpGuoPSxQWPe9+RNAWErrr4NOyW65iO79er9WrntWcRYZIdHCizB1KSqaFiayWGOhETuU8oyqS2u7fMZQyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:17:51.597221Z"},"content_sha256":"17456ec48688fc37a24f79f9b50c2e4b21c614eb48e8127ed8985697212dd478","schema_version":"1.0","event_id":"sha256:17456ec48688fc37a24f79f9b50c2e4b21c614eb48e8127ed8985697212dd478"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BPJ6WDJECAMNWOTBK2RYIQQWHY/bundle.json","state_url":"https://pith.science/pith/BPJ6WDJECAMNWOTBK2RYIQQWHY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BPJ6WDJECAMNWOTBK2RYIQQWHY/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":"2026-08-11T12:17:51Z","links":{"resolver":"https://pith.science/pith/BPJ6WDJECAMNWOTBK2RYIQQWHY","bundle":"https://pith.science/pith/BPJ6WDJECAMNWOTBK2RYIQQWHY/bundle.json","state":"https://pith.science/pith/BPJ6WDJECAMNWOTBK2RYIQQWHY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BPJ6WDJECAMNWOTBK2RYIQQWHY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BPJ6WDJECAMNWOTBK2RYIQQWHY","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":"c2397a344cda0b58e04026c004365de3835d5ed81ba85b1a524f8bd799cb8ba7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-06T18:54:00Z","title_canon_sha256":"f2c9365275e28da17a1efd06bd18b105ccbf5c2dbd44ee283ecfddfc68898c47"},"schema_version":"1.0","source":{"id":"2502.04311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.04311","created_at":"2026-07-05T10:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"2502.04311v1","created_at":"2026-07-05T10:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.04311","created_at":"2026-07-05T10:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"BPJ6WDJECAMN","created_at":"2026-07-05T10:10:36Z"},{"alias_kind":"pith_short_16","alias_value":"BPJ6WDJECAMNWOTB","created_at":"2026-07-05T10:10:36Z"},{"alias_kind":"pith_short_8","alias_value":"BPJ6WDJE","created_at":"2026-07-05T10:10:36Z"}],"graph_snapshots":[{"event_id":"sha256:17456ec48688fc37a24f79f9b50c2e4b21c614eb48e8127ed8985697212dd478","target":"graph","created_at":"2026-07-05T10:10:36Z","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/2502.04311/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we will develop a significantly more general notion of classical Ramsey numbers (extending most other graph-theoretic generalizations) and make some preliminary characterizations of these new Ramsey numbers using simple algebraic tools. Throughout, we make a case arguing that, while our access to specific values of Ramsey numbers (or, in general, precise numerical solutions to Ramsey-theoretic problems) may be limited, the interplay between and overall structure of Ramseyian objects is likely tractable. To support the relevancy of this perspective, we conclude by demonstrating t","authors_text":"Bryce Alan Christopherson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-06T18:54:00Z","title":"Ramsey-Theoretic Characterizations of Classically Non-Ramseyian Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04311","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:f95c7efe471e4b57a5f8c30f185c784f6334692bc33b6357fef52cddbbf6ae20","target":"record","created_at":"2026-07-05T10:10:36Z","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":"c2397a344cda0b58e04026c004365de3835d5ed81ba85b1a524f8bd799cb8ba7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-06T18:54:00Z","title_canon_sha256":"f2c9365275e28da17a1efd06bd18b105ccbf5c2dbd44ee283ecfddfc68898c47"},"schema_version":"1.0","source":{"id":"2502.04311","kind":"arxiv","version":1}},"canonical_sha256":"0bd3eb0d241018db3a6156a38442163e011a12fa147a84b7b3e6b7fa3deed9d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bd3eb0d241018db3a6156a38442163e011a12fa147a84b7b3e6b7fa3deed9d3","first_computed_at":"2026-07-05T10:10:36.629571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:10:36.629571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XEG7IWqrMISMqMiS3ggs+KyTS8l/p6xEIYF0oRn7Stb4UM0cZnDqqey6kwvhCDPa81q5XrteK/SJJH0WjLP9CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:10:36.630027Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.04311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f95c7efe471e4b57a5f8c30f185c784f6334692bc33b6357fef52cddbbf6ae20","sha256:17456ec48688fc37a24f79f9b50c2e4b21c614eb48e8127ed8985697212dd478"],"state_sha256":"ea6e7318a2ed6d43957d269428ab88410fe97095e328c5d9935ea4e8a3ebcd89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pP+XnSTzBlCn7SEz/Dnw6p8N9SvPigEV1JaAW85upSOlGkJEapdbUoXsujXwhda1VnSluqLMP7bvcDtRReFMBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T12:17:51.601508Z","bundle_sha256":"40d0bbc70383144a6b519509bb393f1893ce090cb2fcad13bd425957aa8a27a1"}}