{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6YTFSTKT6HTKCUWC6KQ3JLDZ5M","short_pith_number":"pith:6YTFSTKT","canonical_record":{"source":{"id":"1406.4466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-17T18:27:30Z","cross_cats_sorted":[],"title_canon_sha256":"cb134d6a4ac571062786f00721eacabdce351f3ee485a4e1f08886a79b6006d5","abstract_canon_sha256":"36a7e395881e9189450b77973336f3bc2f4159f9a2f5a4c822f6f7ca188bfe76"},"schema_version":"1.0"},"canonical_sha256":"f626594d53f1e6a152c2f2a1b4ac79eb1133e119761116c5fe4d06bfad520354","source":{"kind":"arxiv","id":"1406.4466","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4466","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4466v1","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4466","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"pith_short_12","alias_value":"6YTFSTKT6HTK","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6YTFSTKT6HTKCUWC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6YTFSTKT","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6YTFSTKT6HTKCUWC6KQ3JLDZ5M","target":"record","payload":{"canonical_record":{"source":{"id":"1406.4466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-17T18:27:30Z","cross_cats_sorted":[],"title_canon_sha256":"cb134d6a4ac571062786f00721eacabdce351f3ee485a4e1f08886a79b6006d5","abstract_canon_sha256":"36a7e395881e9189450b77973336f3bc2f4159f9a2f5a4c822f6f7ca188bfe76"},"schema_version":"1.0"},"canonical_sha256":"f626594d53f1e6a152c2f2a1b4ac79eb1133e119761116c5fe4d06bfad520354","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:31.986062Z","signature_b64":"C+rfwV2sSKcyc7i4H5T/OwGNt3bvgtcipLqBAr4Yhmdr2l2YwmCUvX884hsQJZBFsAQkmMsRNxf3LYYVDyt1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f626594d53f1e6a152c2f2a1b4ac79eb1133e119761116c5fe4d06bfad520354","last_reissued_at":"2026-05-18T02:49:31.985555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:31.985555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.4466","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":"2026-05-18T02:49:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H7XXxOL7BDeBFhw/T/S15TJLepNTQue22a/R4PjOKTnhmYYkKedb9Y/jidL55fklWqDCWVF/mUp+AdrMW4oDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:26:38.354121Z"},"content_sha256":"3c56743f27713a602943a1f6bfb288d2d75396de69b221e123ef313595d8be44","schema_version":"1.0","event_id":"sha256:3c56743f27713a602943a1f6bfb288d2d75396de69b221e123ef313595d8be44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6YTFSTKT6HTKCUWC6KQ3JLDZ5M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On linear equations arising in Combinatorics (Part I)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Masood Aryapoor","submitted_at":"2014-06-17T18:27:30Z","abstract_excerpt":"The main point of this paper is to present a class of equations over integers that one can check if they have a solution by checking a set of inequalities. The prototype of such equations is the equations appearing in the well-known Gale-Ryser theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4466","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":"2026-05-18T02:49:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eB70RJl9ssXmU1Bba4inWsv1LC0G6Zk6aSpl6KjDH5XKwu5q3pnGGJQocR79b6a9VmAyc73QTmkWtopofERqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:26:38.354483Z"},"content_sha256":"e5e9c95e78408052cc32a2b2e8067001fa0f64ef13e04f9e5933e067b781f0e4","schema_version":"1.0","event_id":"sha256:e5e9c95e78408052cc32a2b2e8067001fa0f64ef13e04f9e5933e067b781f0e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6YTFSTKT6HTKCUWC6KQ3JLDZ5M/bundle.json","state_url":"https://pith.science/pith/6YTFSTKT6HTKCUWC6KQ3JLDZ5M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6YTFSTKT6HTKCUWC6KQ3JLDZ5M/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":"2026-06-20T06:26:38Z","links":{"resolver":"https://pith.science/pith/6YTFSTKT6HTKCUWC6KQ3JLDZ5M","bundle":"https://pith.science/pith/6YTFSTKT6HTKCUWC6KQ3JLDZ5M/bundle.json","state":"https://pith.science/pith/6YTFSTKT6HTKCUWC6KQ3JLDZ5M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6YTFSTKT6HTKCUWC6KQ3JLDZ5M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6YTFSTKT6HTKCUWC6KQ3JLDZ5M","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":"36a7e395881e9189450b77973336f3bc2f4159f9a2f5a4c822f6f7ca188bfe76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-17T18:27:30Z","title_canon_sha256":"cb134d6a4ac571062786f00721eacabdce351f3ee485a4e1f08886a79b6006d5"},"schema_version":"1.0","source":{"id":"1406.4466","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4466","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4466v1","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4466","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"pith_short_12","alias_value":"6YTFSTKT6HTK","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6YTFSTKT6HTKCUWC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6YTFSTKT","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:e5e9c95e78408052cc32a2b2e8067001fa0f64ef13e04f9e5933e067b781f0e4","target":"graph","created_at":"2026-05-18T02:49:31Z","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":"The main point of this paper is to present a class of equations over integers that one can check if they have a solution by checking a set of inequalities. The prototype of such equations is the equations appearing in the well-known Gale-Ryser theorem.","authors_text":"Masood Aryapoor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-17T18:27:30Z","title":"On linear equations arising in Combinatorics (Part I)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4466","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":"sha256:3c56743f27713a602943a1f6bfb288d2d75396de69b221e123ef313595d8be44","target":"record","created_at":"2026-05-18T02:49:31Z","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":"36a7e395881e9189450b77973336f3bc2f4159f9a2f5a4c822f6f7ca188bfe76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-17T18:27:30Z","title_canon_sha256":"cb134d6a4ac571062786f00721eacabdce351f3ee485a4e1f08886a79b6006d5"},"schema_version":"1.0","source":{"id":"1406.4466","kind":"arxiv","version":1}},"canonical_sha256":"f626594d53f1e6a152c2f2a1b4ac79eb1133e119761116c5fe4d06bfad520354","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f626594d53f1e6a152c2f2a1b4ac79eb1133e119761116c5fe4d06bfad520354","first_computed_at":"2026-05-18T02:49:31.985555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:31.985555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C+rfwV2sSKcyc7i4H5T/OwGNt3bvgtcipLqBAr4Yhmdr2l2YwmCUvX884hsQJZBFsAQkmMsRNxf3LYYVDyt1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:31.986062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4466","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c56743f27713a602943a1f6bfb288d2d75396de69b221e123ef313595d8be44","sha256:e5e9c95e78408052cc32a2b2e8067001fa0f64ef13e04f9e5933e067b781f0e4"],"state_sha256":"0e13cd9d7706d077ebc349bb70175f4714f7a182415c6bf39f6f222fcbdc9e03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AOpwnMzJi7uCjSNe8coN71uvMS46uu0R85wnJnMzlEdBsZzF1PKh5grCjfcHM4z9oM1/xqaXnfm575DtduAQCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:26:38.356546Z","bundle_sha256":"ab9134b101320da03601515bf9426acb681bc7fb6a208df52924af906e2f9962"}}