{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Y42QGV55HVY5OGOJHBV6K4XUPV","short_pith_number":"pith:Y42QGV55","canonical_record":{"source":{"id":"1112.2322","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-11T05:41:41Z","cross_cats_sorted":[],"title_canon_sha256":"7c57f9f05d110e91c54e6ed84210f99cd8b8775497a2c5b10099d262c994ee53","abstract_canon_sha256":"35e5d9ab8d50068267231344407cfd8c9978035611f105ab03aab80bfaf89d14"},"schema_version":"1.0"},"canonical_sha256":"c7350357bd3d71d719c9386be572f47d7560a2b979aafdbc1821802da66c9e1d","source":{"kind":"arxiv","id":"1112.2322","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2322","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2322v2","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2322","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"Y42QGV55HVY5","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y42QGV55HVY5OGOJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y42QGV55","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Y42QGV55HVY5OGOJHBV6K4XUPV","target":"record","payload":{"canonical_record":{"source":{"id":"1112.2322","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-11T05:41:41Z","cross_cats_sorted":[],"title_canon_sha256":"7c57f9f05d110e91c54e6ed84210f99cd8b8775497a2c5b10099d262c994ee53","abstract_canon_sha256":"35e5d9ab8d50068267231344407cfd8c9978035611f105ab03aab80bfaf89d14"},"schema_version":"1.0"},"canonical_sha256":"c7350357bd3d71d719c9386be572f47d7560a2b979aafdbc1821802da66c9e1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:47.559617Z","signature_b64":"/O8T4XyXXBiQO03Qe7b9EBo6Z5KKJe/hJXNBjUxT7xnA2Y4/liiuusP3pAwRtKcngGYgf+wy88E2+O2AAILEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7350357bd3d71d719c9386be572f47d7560a2b979aafdbc1821802da66c9e1d","last_reissued_at":"2026-05-18T04:05:47.558936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:47.558936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.2322","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":"2026-05-18T04:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kJ+9ohAALozoWJ03jj0OvnsrQLjKc+Hqo5fVh8sM4BVXD+MatGxYDajLQqnDd5aVjoqPiSPT/pB0KLW4yaPGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:09:41.164133Z"},"content_sha256":"04c80c1c0ba38bb005bb4526433e11e7bebbb3914c692b692b0c047250120aed","schema_version":"1.0","event_id":"sha256:04c80c1c0ba38bb005bb4526433e11e7bebbb3914c692b692b0c047250120aed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Y42QGV55HVY5OGOJHBV6K4XUPV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Binomial Theorem for (N + n)^r (where Nf(n)=f(n+1))","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Moa Apagodu, Patrick Gaskill, Shalosh B. Ekhad","submitted_at":"2011-12-11T05:41:41Z","abstract_excerpt":"Binomial Theorem for (N+n)^r is described with non-commuting variables N and n."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2322","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":"2026-05-18T04:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4En5TaY4u2XAF772qsrpBod8buIqWpw4Z9chHAY00+f+ff9kYtwNO8AxdQSGgutLRUM8mLhdSclPmlE/LKOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:09:41.164703Z"},"content_sha256":"984a4c0eb4472877703eaf2f5bddfade408d0b97fd977becc3a8c7c1bc7b05fc","schema_version":"1.0","event_id":"sha256:984a4c0eb4472877703eaf2f5bddfade408d0b97fd977becc3a8c7c1bc7b05fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y42QGV55HVY5OGOJHBV6K4XUPV/bundle.json","state_url":"https://pith.science/pith/Y42QGV55HVY5OGOJHBV6K4XUPV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y42QGV55HVY5OGOJHBV6K4XUPV/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":"2026-05-30T12:09:41Z","links":{"resolver":"https://pith.science/pith/Y42QGV55HVY5OGOJHBV6K4XUPV","bundle":"https://pith.science/pith/Y42QGV55HVY5OGOJHBV6K4XUPV/bundle.json","state":"https://pith.science/pith/Y42QGV55HVY5OGOJHBV6K4XUPV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y42QGV55HVY5OGOJHBV6K4XUPV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Y42QGV55HVY5OGOJHBV6K4XUPV","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":"35e5d9ab8d50068267231344407cfd8c9978035611f105ab03aab80bfaf89d14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-11T05:41:41Z","title_canon_sha256":"7c57f9f05d110e91c54e6ed84210f99cd8b8775497a2c5b10099d262c994ee53"},"schema_version":"1.0","source":{"id":"1112.2322","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2322","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2322v2","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2322","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"Y42QGV55HVY5","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y42QGV55HVY5OGOJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y42QGV55","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:984a4c0eb4472877703eaf2f5bddfade408d0b97fd977becc3a8c7c1bc7b05fc","target":"graph","created_at":"2026-05-18T04:05:47Z","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":"Binomial Theorem for (N+n)^r is described with non-commuting variables N and n.","authors_text":"Moa Apagodu, Patrick Gaskill, Shalosh B. Ekhad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-11T05:41:41Z","title":"The Binomial Theorem for (N + n)^r (where Nf(n)=f(n+1))"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2322","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":"sha256:04c80c1c0ba38bb005bb4526433e11e7bebbb3914c692b692b0c047250120aed","target":"record","created_at":"2026-05-18T04:05:47Z","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":"35e5d9ab8d50068267231344407cfd8c9978035611f105ab03aab80bfaf89d14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-11T05:41:41Z","title_canon_sha256":"7c57f9f05d110e91c54e6ed84210f99cd8b8775497a2c5b10099d262c994ee53"},"schema_version":"1.0","source":{"id":"1112.2322","kind":"arxiv","version":2}},"canonical_sha256":"c7350357bd3d71d719c9386be572f47d7560a2b979aafdbc1821802da66c9e1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7350357bd3d71d719c9386be572f47d7560a2b979aafdbc1821802da66c9e1d","first_computed_at":"2026-05-18T04:05:47.558936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:47.558936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/O8T4XyXXBiQO03Qe7b9EBo6Z5KKJe/hJXNBjUxT7xnA2Y4/liiuusP3pAwRtKcngGYgf+wy88E2+O2AAILEDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:47.559617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2322","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04c80c1c0ba38bb005bb4526433e11e7bebbb3914c692b692b0c047250120aed","sha256:984a4c0eb4472877703eaf2f5bddfade408d0b97fd977becc3a8c7c1bc7b05fc"],"state_sha256":"931e9b26e930e7d7d27521d85f929a18e110c3256bd82ee7bc935a0e8e9e309c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ZCNDlirXmD8IR9HdohIiokx4hR7SMggNoU3xRzUtUEqQXw4tCWxpJ40oxKQOYnlDV6Q6lnebSpw4tXuX93TDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:09:41.168619Z","bundle_sha256":"c4bd573cd158ea7287ea73269c40ec10dc39e88ca33b6df7608ef4c4284ae18f"}}