{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:EIC5K7W5RFTEVHUZ6PANHG5FHA","short_pith_number":"pith:EIC5K7W5","canonical_record":{"source":{"id":"math/0310481","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2003-10-30T22:24:09Z","cross_cats_sorted":[],"title_canon_sha256":"8aaa0bf35ddd45f390d8bbb73155db5403a56025660482f0b4587989b1a33310","abstract_canon_sha256":"87626eef8a672d58c6578bc772142fdc92605612d593ebdee82968f0882c40da"},"schema_version":"1.0"},"canonical_sha256":"2205d57edd89664a9e99f3c0d39ba53805584abe84e62c888c375b5bba945b84","source":{"kind":"arxiv","id":"math/0310481","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0310481","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0310481v1","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0310481","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"EIC5K7W5RFTE","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"EIC5K7W5RFTEVHUZ","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"EIC5K7W5","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:EIC5K7W5RFTEVHUZ6PANHG5FHA","target":"record","payload":{"canonical_record":{"source":{"id":"math/0310481","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2003-10-30T22:24:09Z","cross_cats_sorted":[],"title_canon_sha256":"8aaa0bf35ddd45f390d8bbb73155db5403a56025660482f0b4587989b1a33310","abstract_canon_sha256":"87626eef8a672d58c6578bc772142fdc92605612d593ebdee82968f0882c40da"},"schema_version":"1.0"},"canonical_sha256":"2205d57edd89664a9e99f3c0d39ba53805584abe84e62c888c375b5bba945b84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:00.234649Z","signature_b64":"5syjbkbTDwoUCjE6tHQv/LQBUa2BqYZcqeSvJgl2Ex/ieJi0lvNXywWjBTkmazgO4aWi3IbfDAWdblFDr6NQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2205d57edd89664a9e99f3c0d39ba53805584abe84e62c888c375b5bba945b84","last_reissued_at":"2026-05-18T02:38:00.234175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:00.234175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0310481","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":"2026-05-18T02:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"egAPW4piEaMI3o2L1fLqLaHWA0T1l/Txvyetunl4zthDMDpaJxvTdnLkqFRbZ0ccgarTO1lqPJU65DJnJ438CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:15:27.021453Z"},"content_sha256":"0b3282ac51424312c323848e3a902dae8f3cceacd6b90521092ae8d2ab1abae7","schema_version":"1.0","event_id":"sha256:0b3282ac51424312c323848e3a902dae8f3cceacd6b90521092ae8d2ab1abae7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:EIC5K7W5RFTEVHUZ6PANHG5FHA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calculus III: Taylor Series","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Thomas G. Goodwillie","submitted_at":"2003-10-30T22:24:09Z","abstract_excerpt":"We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal n-excisive approximation, which may be thought of as its n-excisive part. Homogeneous functors, meaning n-excisive functors with trivial (n-1)-excisive part, can be classified: they correspond to symmetric functors of n variables that are reduced and 1-excisive in each variable. We discuss some important examples, including the identity functor and Waldhausen's algebraic K-theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0310481","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":"2026-05-18T02:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L6hr9HpuRsY9XEgUj2UdJUXRWrk3ePyJjzjz+9H7GAejV74DnrqqggPWtfEIT0LtkYBUlF3K477KQq7UVsjQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:15:27.021800Z"},"content_sha256":"9602625a8935c5497eed4e3e9ed1a9e6bb7394528f79cf8bd8cf3267e28ca914","schema_version":"1.0","event_id":"sha256:9602625a8935c5497eed4e3e9ed1a9e6bb7394528f79cf8bd8cf3267e28ca914"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EIC5K7W5RFTEVHUZ6PANHG5FHA/bundle.json","state_url":"https://pith.science/pith/EIC5K7W5RFTEVHUZ6PANHG5FHA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EIC5K7W5RFTEVHUZ6PANHG5FHA/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":"2026-06-26T16:15:27Z","links":{"resolver":"https://pith.science/pith/EIC5K7W5RFTEVHUZ6PANHG5FHA","bundle":"https://pith.science/pith/EIC5K7W5RFTEVHUZ6PANHG5FHA/bundle.json","state":"https://pith.science/pith/EIC5K7W5RFTEVHUZ6PANHG5FHA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EIC5K7W5RFTEVHUZ6PANHG5FHA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:EIC5K7W5RFTEVHUZ6PANHG5FHA","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":"87626eef8a672d58c6578bc772142fdc92605612d593ebdee82968f0882c40da","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2003-10-30T22:24:09Z","title_canon_sha256":"8aaa0bf35ddd45f390d8bbb73155db5403a56025660482f0b4587989b1a33310"},"schema_version":"1.0","source":{"id":"math/0310481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0310481","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0310481v1","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0310481","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"EIC5K7W5RFTE","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"EIC5K7W5RFTEVHUZ","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"EIC5K7W5","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:9602625a8935c5497eed4e3e9ed1a9e6bb7394528f79cf8bd8cf3267e28ca914","target":"graph","created_at":"2026-05-18T02:38:00Z","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 study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal n-excisive approximation, which may be thought of as its n-excisive part. Homogeneous functors, meaning n-excisive functors with trivial (n-1)-excisive part, can be classified: they correspond to symmetric functors of n variables that are reduced and 1-excisive in each variable. We discuss some important examples, including the identity functor and Waldhausen's algebraic K-theory.","authors_text":"Thomas G. Goodwillie","cross_cats":[],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2003-10-30T22:24:09Z","title":"Calculus III: Taylor Series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0310481","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":"sha256:0b3282ac51424312c323848e3a902dae8f3cceacd6b90521092ae8d2ab1abae7","target":"record","created_at":"2026-05-18T02:38:00Z","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":"87626eef8a672d58c6578bc772142fdc92605612d593ebdee82968f0882c40da","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2003-10-30T22:24:09Z","title_canon_sha256":"8aaa0bf35ddd45f390d8bbb73155db5403a56025660482f0b4587989b1a33310"},"schema_version":"1.0","source":{"id":"math/0310481","kind":"arxiv","version":1}},"canonical_sha256":"2205d57edd89664a9e99f3c0d39ba53805584abe84e62c888c375b5bba945b84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2205d57edd89664a9e99f3c0d39ba53805584abe84e62c888c375b5bba945b84","first_computed_at":"2026-05-18T02:38:00.234175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:00.234175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5syjbkbTDwoUCjE6tHQv/LQBUa2BqYZcqeSvJgl2Ex/ieJi0lvNXywWjBTkmazgO4aWi3IbfDAWdblFDr6NQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:00.234649Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0310481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b3282ac51424312c323848e3a902dae8f3cceacd6b90521092ae8d2ab1abae7","sha256:9602625a8935c5497eed4e3e9ed1a9e6bb7394528f79cf8bd8cf3267e28ca914"],"state_sha256":"6ef2068dc6b2ed184133fba08ef2774dbccd6e2d0c532078056b2985c2447e1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GftuPnmB83MqVn+APblbjgZ6Q148EzW7IOGSRziC2ttOo985bi8uTfLpNycB6NzKjvYYaXqhdal+51WeUL2RAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T16:15:27.024921Z","bundle_sha256":"097f966d9ee42875e2597e60fce8c8b1be9a687832b9adcf72937fd44788aa0e"}}