{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:77EQQBFJCBQINXGWEPDCRSMKLD","short_pith_number":"pith:77EQQBFJ","canonical_record":{"source":{"id":"1611.04910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-15T16:06:40Z","cross_cats_sorted":[],"title_canon_sha256":"28f1e2967cb1f023ddc9fa3684681aea88f01c3d2d4136c6fea8c56e8a2f82e0","abstract_canon_sha256":"0781515ee1a70313a4402fd6c49f875da768e66a4a2da16b075d30bbf726c8bf"},"schema_version":"1.0"},"canonical_sha256":"ffc90804a9106086dcd623c628c98a58d15310733655c7f4f29213b9378ff866","source":{"kind":"arxiv","id":"1611.04910","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04910","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04910v2","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04910","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"77EQQBFJCBQI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"77EQQBFJCBQINXGW","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"77EQQBFJ","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:77EQQBFJCBQINXGWEPDCRSMKLD","target":"record","payload":{"canonical_record":{"source":{"id":"1611.04910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-15T16:06:40Z","cross_cats_sorted":[],"title_canon_sha256":"28f1e2967cb1f023ddc9fa3684681aea88f01c3d2d4136c6fea8c56e8a2f82e0","abstract_canon_sha256":"0781515ee1a70313a4402fd6c49f875da768e66a4a2da16b075d30bbf726c8bf"},"schema_version":"1.0"},"canonical_sha256":"ffc90804a9106086dcd623c628c98a58d15310733655c7f4f29213b9378ff866","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:04.592311Z","signature_b64":"LdgyRKG0r6eefd6eZCVD5iHhT/CZo2FjAZdrQ80oNWMt9nI2no68G6OnyWoEq9BLYCJZlYOM2iDtCm56ARlZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffc90804a9106086dcd623c628c98a58d15310733655c7f4f29213b9378ff866","last_reissued_at":"2026-05-18T00:54:04.591833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:04.591833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.04910","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":"2026-05-18T00:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dgkh6urWpvudBODqIaIeQ4UY+HEbPNc7OeiBxW5wu37FZ0HZiWNaECPDN1uwtJL98TipJafBYsOwboVaNRFhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:56:12.636112Z"},"content_sha256":"e1a9db6a3c945fc27f39c8ed755795528fea019d667c88b71e5917caeffaf4e9","schema_version":"1.0","event_id":"sha256:e1a9db6a3c945fc27f39c8ed755795528fea019d667c88b71e5917caeffaf4e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:77EQQBFJCBQINXGWEPDCRSMKLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic density of Motzkin numbers modulo small primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rob Burns","submitted_at":"2016-11-15T16:06:40Z","abstract_excerpt":"We establish the asymptotic density of the Motzkin numbers modulo small primes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04910","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":"2026-05-18T00:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gv86t3nYt1kVV2nQKBDH9aG0ZT7reoyQkeUafSYBsmOOsoIrOU9n/LDJ9HnF9t4CvQ9viR89+j28r2dkEcO/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:56:12.636842Z"},"content_sha256":"a095e5aa01a58e6eb503bb7934bc58f6053ac838ef7a91ba4beea2a4efd61cdc","schema_version":"1.0","event_id":"sha256:a095e5aa01a58e6eb503bb7934bc58f6053ac838ef7a91ba4beea2a4efd61cdc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/77EQQBFJCBQINXGWEPDCRSMKLD/bundle.json","state_url":"https://pith.science/pith/77EQQBFJCBQINXGWEPDCRSMKLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/77EQQBFJCBQINXGWEPDCRSMKLD/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":"2026-06-09T01:56:12Z","links":{"resolver":"https://pith.science/pith/77EQQBFJCBQINXGWEPDCRSMKLD","bundle":"https://pith.science/pith/77EQQBFJCBQINXGWEPDCRSMKLD/bundle.json","state":"https://pith.science/pith/77EQQBFJCBQINXGWEPDCRSMKLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/77EQQBFJCBQINXGWEPDCRSMKLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:77EQQBFJCBQINXGWEPDCRSMKLD","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":"0781515ee1a70313a4402fd6c49f875da768e66a4a2da16b075d30bbf726c8bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-15T16:06:40Z","title_canon_sha256":"28f1e2967cb1f023ddc9fa3684681aea88f01c3d2d4136c6fea8c56e8a2f82e0"},"schema_version":"1.0","source":{"id":"1611.04910","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04910","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04910v2","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04910","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"77EQQBFJCBQI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"77EQQBFJCBQINXGW","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"77EQQBFJ","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:a095e5aa01a58e6eb503bb7934bc58f6053ac838ef7a91ba4beea2a4efd61cdc","target":"graph","created_at":"2026-05-18T00:54:04Z","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 establish the asymptotic density of the Motzkin numbers modulo small primes.","authors_text":"Rob Burns","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-15T16:06:40Z","title":"Asymptotic density of Motzkin numbers modulo small primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04910","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:e1a9db6a3c945fc27f39c8ed755795528fea019d667c88b71e5917caeffaf4e9","target":"record","created_at":"2026-05-18T00:54:04Z","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":"0781515ee1a70313a4402fd6c49f875da768e66a4a2da16b075d30bbf726c8bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-15T16:06:40Z","title_canon_sha256":"28f1e2967cb1f023ddc9fa3684681aea88f01c3d2d4136c6fea8c56e8a2f82e0"},"schema_version":"1.0","source":{"id":"1611.04910","kind":"arxiv","version":2}},"canonical_sha256":"ffc90804a9106086dcd623c628c98a58d15310733655c7f4f29213b9378ff866","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffc90804a9106086dcd623c628c98a58d15310733655c7f4f29213b9378ff866","first_computed_at":"2026-05-18T00:54:04.591833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:04.591833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LdgyRKG0r6eefd6eZCVD5iHhT/CZo2FjAZdrQ80oNWMt9nI2no68G6OnyWoEq9BLYCJZlYOM2iDtCm56ARlZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:04.592311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04910","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1a9db6a3c945fc27f39c8ed755795528fea019d667c88b71e5917caeffaf4e9","sha256:a095e5aa01a58e6eb503bb7934bc58f6053ac838ef7a91ba4beea2a4efd61cdc"],"state_sha256":"95c0e50b7d74a34308dd4df20f33c51fe7bfbcd24d1683dba0d2f6a9ab556cb9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTFOgdo0VjLougUS//qGt5fqGOenMeHxddw4Hqs3WAIJ6+DKRSjmD0i86nKbWVTrKcCCO3u4xoqI4eMufDxrAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T01:56:12.641071Z","bundle_sha256":"9a2e22527aadf6ac693de77dbdfde85c6c1a1fff89d55837464fa90b7adc5aea"}}