{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XYD3UAG6OZI77GLLUPQTLGVSUH","short_pith_number":"pith:XYD3UAG6","canonical_record":{"source":{"id":"1503.04240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-13T22:47:04Z","cross_cats_sorted":[],"title_canon_sha256":"630dd134d48102e6b0550e561e60f486c3b37bd05868fa6dfb3a15255180c8de","abstract_canon_sha256":"7c12cbf572c8db7211d0f6cc13175f9a58bbf4e6aae5a3befba38165dba1996b"},"schema_version":"1.0"},"canonical_sha256":"be07ba00de7651ff996ba3e1359ab2a1d863ec21f4eb5e0defea824cfab7729d","source":{"kind":"arxiv","id":"1503.04240","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04240","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04240v1","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04240","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"pith_short_12","alias_value":"XYD3UAG6OZI7","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XYD3UAG6OZI77GLL","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XYD3UAG6","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XYD3UAG6OZI77GLLUPQTLGVSUH","target":"record","payload":{"canonical_record":{"source":{"id":"1503.04240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-13T22:47:04Z","cross_cats_sorted":[],"title_canon_sha256":"630dd134d48102e6b0550e561e60f486c3b37bd05868fa6dfb3a15255180c8de","abstract_canon_sha256":"7c12cbf572c8db7211d0f6cc13175f9a58bbf4e6aae5a3befba38165dba1996b"},"schema_version":"1.0"},"canonical_sha256":"be07ba00de7651ff996ba3e1359ab2a1d863ec21f4eb5e0defea824cfab7729d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:25.714010Z","signature_b64":"1aK6uziABkqcNvfX2bSbThvSeI3E0xkW94x26PEmcbmIlZWLCvkMQS0iJyzTPKCGjpX48w/VRBHpDfJaHjXkDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be07ba00de7651ff996ba3e1359ab2a1d863ec21f4eb5e0defea824cfab7729d","last_reissued_at":"2026-05-18T02:23:25.713379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:25.713379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.04240","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":"2026-05-18T02:23:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BC3lOlzYCayoj9oAWoXD7yRBFmW92sfDQpQ5RL+pYQt3xctGvZkl97cV4jLOUqaKL7wt+SZveWKN8nt5UVLoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:34:36.899119Z"},"content_sha256":"0b9aac373af1831346ec72a27cc82b6c6345dd998072957510cc11fd75f1ebd4","schema_version":"1.0","event_id":"sha256:0b9aac373af1831346ec72a27cc82b6c6345dd998072957510cc11fd75f1ebd4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XYD3UAG6OZI77GLLUPQTLGVSUH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The many faces of modern combinatorics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cristian Lenart","submitted_at":"2015-03-13T22:47:04Z","abstract_excerpt":"This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including algebraic geometry), topology, probability theory, and theoretical computer science."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04240","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":"2026-05-18T02:23:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xdlZQUmhxdv3dcX6VKfnpJ/+Khcjb4zdE5yDKbt2kZ6MVEJFbZ+EiIenxEFstdlobNcmLVa9UfvJBMX1LOFPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:34:36.899721Z"},"content_sha256":"0f7624de2884658778f0c4a3b47a8776931d52db358263a2798a903cfda2f42c","schema_version":"1.0","event_id":"sha256:0f7624de2884658778f0c4a3b47a8776931d52db358263a2798a903cfda2f42c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XYD3UAG6OZI77GLLUPQTLGVSUH/bundle.json","state_url":"https://pith.science/pith/XYD3UAG6OZI77GLLUPQTLGVSUH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XYD3UAG6OZI77GLLUPQTLGVSUH/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":"2026-06-07T21:34:36Z","links":{"resolver":"https://pith.science/pith/XYD3UAG6OZI77GLLUPQTLGVSUH","bundle":"https://pith.science/pith/XYD3UAG6OZI77GLLUPQTLGVSUH/bundle.json","state":"https://pith.science/pith/XYD3UAG6OZI77GLLUPQTLGVSUH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XYD3UAG6OZI77GLLUPQTLGVSUH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XYD3UAG6OZI77GLLUPQTLGVSUH","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":"7c12cbf572c8db7211d0f6cc13175f9a58bbf4e6aae5a3befba38165dba1996b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-13T22:47:04Z","title_canon_sha256":"630dd134d48102e6b0550e561e60f486c3b37bd05868fa6dfb3a15255180c8de"},"schema_version":"1.0","source":{"id":"1503.04240","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04240","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04240v1","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04240","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"pith_short_12","alias_value":"XYD3UAG6OZI7","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XYD3UAG6OZI77GLL","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XYD3UAG6","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:0f7624de2884658778f0c4a3b47a8776931d52db358263a2798a903cfda2f42c","target":"graph","created_at":"2026-05-18T02:23:25Z","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 is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including algebraic geometry), topology, probability theory, and theoretical computer science.","authors_text":"Cristian Lenart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-13T22:47:04Z","title":"The many faces of modern combinatorics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04240","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":"sha256:0b9aac373af1831346ec72a27cc82b6c6345dd998072957510cc11fd75f1ebd4","target":"record","created_at":"2026-05-18T02:23:25Z","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":"7c12cbf572c8db7211d0f6cc13175f9a58bbf4e6aae5a3befba38165dba1996b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-13T22:47:04Z","title_canon_sha256":"630dd134d48102e6b0550e561e60f486c3b37bd05868fa6dfb3a15255180c8de"},"schema_version":"1.0","source":{"id":"1503.04240","kind":"arxiv","version":1}},"canonical_sha256":"be07ba00de7651ff996ba3e1359ab2a1d863ec21f4eb5e0defea824cfab7729d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be07ba00de7651ff996ba3e1359ab2a1d863ec21f4eb5e0defea824cfab7729d","first_computed_at":"2026-05-18T02:23:25.713379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:25.713379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1aK6uziABkqcNvfX2bSbThvSeI3E0xkW94x26PEmcbmIlZWLCvkMQS0iJyzTPKCGjpX48w/VRBHpDfJaHjXkDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:25.714010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04240","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b9aac373af1831346ec72a27cc82b6c6345dd998072957510cc11fd75f1ebd4","sha256:0f7624de2884658778f0c4a3b47a8776931d52db358263a2798a903cfda2f42c"],"state_sha256":"be1e34a4b294f060ba276622683676a3242dec6174203f11289dd8541a82982f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JAC2Cjir0OQkp8RBDwQZ/24XAkbUJal9WvBfEBJJCCBYmcAMQJbA7AazYVzwKsVixqt/Z6Fh6O4j7xqr0B+IDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:34:36.903118Z","bundle_sha256":"9c48aad1970838ecf86bd42bd303dc5f9d12ba69df938d59c0a9195e16472505"}}