{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PQ4TKEALKPZZXYEPBISW5TVR54","short_pith_number":"pith:PQ4TKEAL","canonical_record":{"source":{"id":"1509.06286","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-21T16:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"c3fa20965b7e78140a4464b7c97cdda3105ac7d8bddb432a70c9a407d86653cf","abstract_canon_sha256":"4ece02fc3854ad0d8cf3db6cbfe4a3b0623ca83205c51655dadd652288c92f6b"},"schema_version":"1.0"},"canonical_sha256":"7c3935100b53f39be08f0a256eceb1ef137c5e5777a86552fbacdeec8b52a31f","source":{"kind":"arxiv","id":"1509.06286","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06286","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06286v2","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06286","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"pith_short_12","alias_value":"PQ4TKEALKPZZ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PQ4TKEALKPZZXYEP","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PQ4TKEAL","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PQ4TKEALKPZZXYEPBISW5TVR54","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06286","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-21T16:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"c3fa20965b7e78140a4464b7c97cdda3105ac7d8bddb432a70c9a407d86653cf","abstract_canon_sha256":"4ece02fc3854ad0d8cf3db6cbfe4a3b0623ca83205c51655dadd652288c92f6b"},"schema_version":"1.0"},"canonical_sha256":"7c3935100b53f39be08f0a256eceb1ef137c5e5777a86552fbacdeec8b52a31f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:08.417633Z","signature_b64":"M7FbiySNpIwLLXxTwaVdWiXJxD4y+HL+wsGvtOCXOlGVUgn6DtmVAVmiTMII3pDkYEOGOP2SRxY6oQ1gP3AOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c3935100b53f39be08f0a256eceb1ef137c5e5777a86552fbacdeec8b52a31f","last_reissued_at":"2026-05-18T00:46:08.417114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:08.417114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06286","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":"2026-05-18T00:46:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mwexgargy7GdIOY6Oq4f9Hv904R9ufjcRepWgtaSp3UPqZgCELZkXOgTiYVQeMnZdFjXFlPjupKVbJr3W+BqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:07:55.818712Z"},"content_sha256":"8913808fe6943494739e4943dac66581c0805d280151167400dd7155660a2d29","schema_version":"1.0","event_id":"sha256:8913808fe6943494739e4943dac66581c0805d280151167400dd7155660a2d29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PQ4TKEALKPZZXYEPBISW5TVR54","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"There is no strongly regular graph with parameters (460,153,32,60)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Mellit, A. Prymak, A. V. Bondarenko, D. Radchenko, M. Viazovska","submitted_at":"2015-09-21T16:10:31Z","abstract_excerpt":"We prove that there is no strongly regular graph (SRG) with parameters (460,153,32,60). The proof is based on a recent lower bound on the number of 4-cliques in a SRG and some applications of Euclidean representation of SRGs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06286","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":""},"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":"2026-05-18T00:46:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ASfj1j+fYwGrDGW2Cy+DQhyQX0lsoJTcKlJ3FfTmXBqukSems/CNQGO6igoiifiZv7cZVnVT3JRRwP5O99FeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:07:55.819050Z"},"content_sha256":"d76a46aa31c5f1d30f50cc146a201f4c246c1e5efc0ec611732f17c44abca1d0","schema_version":"1.0","event_id":"sha256:d76a46aa31c5f1d30f50cc146a201f4c246c1e5efc0ec611732f17c44abca1d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQ4TKEALKPZZXYEPBISW5TVR54/bundle.json","state_url":"https://pith.science/pith/PQ4TKEALKPZZXYEPBISW5TVR54/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQ4TKEALKPZZXYEPBISW5TVR54/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":"2026-06-11T11:07:55Z","links":{"resolver":"https://pith.science/pith/PQ4TKEALKPZZXYEPBISW5TVR54","bundle":"https://pith.science/pith/PQ4TKEALKPZZXYEPBISW5TVR54/bundle.json","state":"https://pith.science/pith/PQ4TKEALKPZZXYEPBISW5TVR54/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQ4TKEALKPZZXYEPBISW5TVR54/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PQ4TKEALKPZZXYEPBISW5TVR54","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":"4ece02fc3854ad0d8cf3db6cbfe4a3b0623ca83205c51655dadd652288c92f6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-21T16:10:31Z","title_canon_sha256":"c3fa20965b7e78140a4464b7c97cdda3105ac7d8bddb432a70c9a407d86653cf"},"schema_version":"1.0","source":{"id":"1509.06286","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06286","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06286v2","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06286","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"pith_short_12","alias_value":"PQ4TKEALKPZZ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PQ4TKEALKPZZXYEP","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PQ4TKEAL","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:d76a46aa31c5f1d30f50cc146a201f4c246c1e5efc0ec611732f17c44abca1d0","target":"graph","created_at":"2026-05-18T00:46:08Z","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 prove that there is no strongly regular graph (SRG) with parameters (460,153,32,60). The proof is based on a recent lower bound on the number of 4-cliques in a SRG and some applications of Euclidean representation of SRGs.","authors_text":"A. Mellit, A. Prymak, A. V. Bondarenko, D. Radchenko, M. Viazovska","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-21T16:10:31Z","title":"There is no strongly regular graph with parameters (460,153,32,60)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06286","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":"sha256:8913808fe6943494739e4943dac66581c0805d280151167400dd7155660a2d29","target":"record","created_at":"2026-05-18T00:46:08Z","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":"4ece02fc3854ad0d8cf3db6cbfe4a3b0623ca83205c51655dadd652288c92f6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-21T16:10:31Z","title_canon_sha256":"c3fa20965b7e78140a4464b7c97cdda3105ac7d8bddb432a70c9a407d86653cf"},"schema_version":"1.0","source":{"id":"1509.06286","kind":"arxiv","version":2}},"canonical_sha256":"7c3935100b53f39be08f0a256eceb1ef137c5e5777a86552fbacdeec8b52a31f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c3935100b53f39be08f0a256eceb1ef137c5e5777a86552fbacdeec8b52a31f","first_computed_at":"2026-05-18T00:46:08.417114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:08.417114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M7FbiySNpIwLLXxTwaVdWiXJxD4y+HL+wsGvtOCXOlGVUgn6DtmVAVmiTMII3pDkYEOGOP2SRxY6oQ1gP3AOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:08.417633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06286","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8913808fe6943494739e4943dac66581c0805d280151167400dd7155660a2d29","sha256:d76a46aa31c5f1d30f50cc146a201f4c246c1e5efc0ec611732f17c44abca1d0"],"state_sha256":"88c0ef8f98d39bf9ec0de5fb41e96f5d395b7df83af9bc12646388dcf21d2fd3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVjTc7v/p0CW0bSLbOUktHxPRHQ7c3UxIzFrAtAwQj4aLdwWwdlquLOng6FD7+86drmAyZPoNAG7u8NkYIUYAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:07:55.820946Z","bundle_sha256":"742a740254a2e962dc9f398be5de503a6e2bb31a7f15007b1012d039483c71d7"}}