{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PRYPGV7I57ANYQWDN5TMM2FXPP","short_pith_number":"pith:PRYPGV7I","canonical_record":{"source":{"id":"1202.6537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-02-29T13:14:26Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fed2e067dae7bbb67a6f35fa2f1e75a27501b1fd4b74b2d4409750b53b9dd930","abstract_canon_sha256":"268775a9ffa89cc01dc4fc15092bc5adc32d9b0e7fbcdf35fea30d900b6a7687"},"schema_version":"1.0"},"canonical_sha256":"7c70f357e8efc0dc42c36f66c668b77bf9352cf1eb61dcbe49dca5231f91a70a","source":{"kind":"arxiv","id":"1202.6537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6537","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6537v1","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6537","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"PRYPGV7I57AN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PRYPGV7I57ANYQWD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PRYPGV7I","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PRYPGV7I57ANYQWDN5TMM2FXPP","target":"record","payload":{"canonical_record":{"source":{"id":"1202.6537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-02-29T13:14:26Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fed2e067dae7bbb67a6f35fa2f1e75a27501b1fd4b74b2d4409750b53b9dd930","abstract_canon_sha256":"268775a9ffa89cc01dc4fc15092bc5adc32d9b0e7fbcdf35fea30d900b6a7687"},"schema_version":"1.0"},"canonical_sha256":"7c70f357e8efc0dc42c36f66c668b77bf9352cf1eb61dcbe49dca5231f91a70a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:41.531435Z","signature_b64":"UOytZrsk77j5SdoPyUvmF4n5LS30zLkq+RQZYk1qqLhGBg1dN8YF0JWaUvpZbjJs7JfBEB4FKqdVy1rJJawVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c70f357e8efc0dc42c36f66c668b77bf9352cf1eb61dcbe49dca5231f91a70a","last_reissued_at":"2026-05-18T03:45:41.530688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:41.530688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.6537","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":"2026-05-18T03:45:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PHxkRmKafykfLz85jCoouORLK0o7Ae3xrUiuid+gk2FGEv45d874bd7FsZq2kqd8XChpbT3d6lVES9y+coIuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:55:37.341273Z"},"content_sha256":"84da08d52a0126c701d70d3dbd13784c72ecb7d2a2a9213d1495404ee90d1695","schema_version":"1.0","event_id":"sha256:84da08d52a0126c701d70d3dbd13784c72ecb7d2a2a9213d1495404ee90d1695"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PRYPGV7I57ANYQWDN5TMM2FXPP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Divided Differences of Multivariate Implicit Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NA","authors_text":"Georg Muntingh","submitted_at":"2012-02-29T13:14:26Z","abstract_excerpt":"Under general conditions, the equation $g(x^1, ..., x^q, y) = 0$ implicitly defines $y$ locally as a function of $x^1, ..., x^q$. In this article, we express divided differences of $y$ in terms of divided differences of $g$, generalizing a recent formula for the case where $y$ is univariate. The formula involves a sum over a combinatorial structure whose elements can be viewed either as polygonal partitions or as plane trees. Through this connection we prove as a corollary a formula for derivatives of $y$ in terms of derivatives of $g$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6537","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":"2026-05-18T03:45:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CPBQfQd4t/xGw+PAXzmV4nlJ833wet8m7uV/0aYaOOXjDYuv6Nh+BzKJASvaOlsh7dT+vtWwL8ua/8aJeEKpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:55:37.341655Z"},"content_sha256":"9df3242c0bf56b5de7dfee535e53ea8b3fc8d9b5bb260afab230e6af088d7257","schema_version":"1.0","event_id":"sha256:9df3242c0bf56b5de7dfee535e53ea8b3fc8d9b5bb260afab230e6af088d7257"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PRYPGV7I57ANYQWDN5TMM2FXPP/bundle.json","state_url":"https://pith.science/pith/PRYPGV7I57ANYQWDN5TMM2FXPP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PRYPGV7I57ANYQWDN5TMM2FXPP/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":"2026-05-28T14:55:37Z","links":{"resolver":"https://pith.science/pith/PRYPGV7I57ANYQWDN5TMM2FXPP","bundle":"https://pith.science/pith/PRYPGV7I57ANYQWDN5TMM2FXPP/bundle.json","state":"https://pith.science/pith/PRYPGV7I57ANYQWDN5TMM2FXPP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PRYPGV7I57ANYQWDN5TMM2FXPP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PRYPGV7I57ANYQWDN5TMM2FXPP","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":"268775a9ffa89cc01dc4fc15092bc5adc32d9b0e7fbcdf35fea30d900b6a7687","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-02-29T13:14:26Z","title_canon_sha256":"fed2e067dae7bbb67a6f35fa2f1e75a27501b1fd4b74b2d4409750b53b9dd930"},"schema_version":"1.0","source":{"id":"1202.6537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6537","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6537v1","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6537","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"PRYPGV7I57AN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PRYPGV7I57ANYQWD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PRYPGV7I","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:9df3242c0bf56b5de7dfee535e53ea8b3fc8d9b5bb260afab230e6af088d7257","target":"graph","created_at":"2026-05-18T03:45:41Z","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":"Under general conditions, the equation $g(x^1, ..., x^q, y) = 0$ implicitly defines $y$ locally as a function of $x^1, ..., x^q$. In this article, we express divided differences of $y$ in terms of divided differences of $g$, generalizing a recent formula for the case where $y$ is univariate. The formula involves a sum over a combinatorial structure whose elements can be viewed either as polygonal partitions or as plane trees. Through this connection we prove as a corollary a formula for derivatives of $y$ in terms of derivatives of $g$.","authors_text":"Georg Muntingh","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-02-29T13:14:26Z","title":"Divided Differences of Multivariate Implicit Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6537","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":"sha256:84da08d52a0126c701d70d3dbd13784c72ecb7d2a2a9213d1495404ee90d1695","target":"record","created_at":"2026-05-18T03:45:41Z","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":"268775a9ffa89cc01dc4fc15092bc5adc32d9b0e7fbcdf35fea30d900b6a7687","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-02-29T13:14:26Z","title_canon_sha256":"fed2e067dae7bbb67a6f35fa2f1e75a27501b1fd4b74b2d4409750b53b9dd930"},"schema_version":"1.0","source":{"id":"1202.6537","kind":"arxiv","version":1}},"canonical_sha256":"7c70f357e8efc0dc42c36f66c668b77bf9352cf1eb61dcbe49dca5231f91a70a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c70f357e8efc0dc42c36f66c668b77bf9352cf1eb61dcbe49dca5231f91a70a","first_computed_at":"2026-05-18T03:45:41.530688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:41.530688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UOytZrsk77j5SdoPyUvmF4n5LS30zLkq+RQZYk1qqLhGBg1dN8YF0JWaUvpZbjJs7JfBEB4FKqdVy1rJJawVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:41.531435Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84da08d52a0126c701d70d3dbd13784c72ecb7d2a2a9213d1495404ee90d1695","sha256:9df3242c0bf56b5de7dfee535e53ea8b3fc8d9b5bb260afab230e6af088d7257"],"state_sha256":"d828e4b1c1ba956274b19366b68400bef488fcfdef7e61998a01984721ce2643"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9QCm8MDN/dUFt6h525MkaleBmAu6JIox+bNjEvgOIcC8BHSxiujQW4HCowFoZpmlJlDSdasBejcqe8GKyZC7Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:55:37.343819Z","bundle_sha256":"f52a17a2751160f0b16c5b9851c41672f07e619ea6efc6e749622958262b7c39"}}