{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NRZQHJNXSREX7MK5P7URAQZQY7","short_pith_number":"pith:NRZQHJNX","canonical_record":{"source":{"id":"1610.03127","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-10T23:28:00Z","cross_cats_sorted":[],"title_canon_sha256":"bc6ba93f171fa5d7477990810e4c1cb6b1301d952c794ed76f825fbc42b374ef","abstract_canon_sha256":"d742dd797d0dc94bfb67abe6ddd074cb0b6d5a19a989e081698477ee96031c3c"},"schema_version":"1.0"},"canonical_sha256":"6c7303a5b794497fb15d7fe9104330c7e3e5a22c48bdc80b359b77111ec1a642","source":{"kind":"arxiv","id":"1610.03127","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03127","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03127v3","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03127","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"NRZQHJNXSREX","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NRZQHJNXSREX7MK5","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NRZQHJNX","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NRZQHJNXSREX7MK5P7URAQZQY7","target":"record","payload":{"canonical_record":{"source":{"id":"1610.03127","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-10T23:28:00Z","cross_cats_sorted":[],"title_canon_sha256":"bc6ba93f171fa5d7477990810e4c1cb6b1301d952c794ed76f825fbc42b374ef","abstract_canon_sha256":"d742dd797d0dc94bfb67abe6ddd074cb0b6d5a19a989e081698477ee96031c3c"},"schema_version":"1.0"},"canonical_sha256":"6c7303a5b794497fb15d7fe9104330c7e3e5a22c48bdc80b359b77111ec1a642","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:08.540001Z","signature_b64":"YLhxSXRxTETRPa9EM1/cOZP7RkGO7wBCk/wyu33wOHBCxEBLUr39tb3SYP77wcjL0HEXwmGKlQhgJ2ZATm6vAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c7303a5b794497fb15d7fe9104330c7e3e5a22c48bdc80b359b77111ec1a642","last_reissued_at":"2026-05-18T00:04:08.539272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:08.539272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.03127","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SwnGWYp9zJ9JPDqMpfrBnymMPDJTOhVfSHUzIvIV1md4lyFEK1HvUjQiHWXra9oZokpZqL6CYEUN/tRRWEi6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:20:44.930292Z"},"content_sha256":"4a0dfda37c1137a63616fd08ec44be74c81ab13e7635708cf2cb67a8f777f771","schema_version":"1.0","event_id":"sha256:4a0dfda37c1137a63616fd08ec44be74c81ab13e7635708cf2cb67a8f777f771"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NRZQHJNXSREX7MK5P7URAQZQY7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Goodwillie calculus and Mackey functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Saul Glasman","submitted_at":"2016-10-10T23:28:00Z","abstract_excerpt":"We show that the category of $n$-excisive functors from the $\\infty$-category of spectra to a target stable $\\infty$-category $\\mathbf{E}$ is equivalent to the category of $\\mathbf{E}$-valued Mackey functors on an indexing category built from finite sets and surjections. This new classification of polynomial functors arises from an investigation of the structure present on cross effects. The path to this result involves a pair of surprising extension theorems for polynomial functors and a discussion of some interesting topics in semiadditive $\\infty$- category theory, including a formula for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03127","kind":"arxiv","version":3},"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":"2026-05-18T00:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f0AhmHYEinY5r8H90EmiJDXWRmhVDwt9107tJ3PvJfsQLQBK5r5c45KOrwCbCRpj83EqpdwIzBhjLlwiC/JfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:20:44.930975Z"},"content_sha256":"cc8389b018513dc118672ecdb56ab4a4d1d45e69b52e8c60aee11ea1baae3c90","schema_version":"1.0","event_id":"sha256:cc8389b018513dc118672ecdb56ab4a4d1d45e69b52e8c60aee11ea1baae3c90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NRZQHJNXSREX7MK5P7URAQZQY7/bundle.json","state_url":"https://pith.science/pith/NRZQHJNXSREX7MK5P7URAQZQY7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NRZQHJNXSREX7MK5P7URAQZQY7/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":"2026-06-09T09:20:44Z","links":{"resolver":"https://pith.science/pith/NRZQHJNXSREX7MK5P7URAQZQY7","bundle":"https://pith.science/pith/NRZQHJNXSREX7MK5P7URAQZQY7/bundle.json","state":"https://pith.science/pith/NRZQHJNXSREX7MK5P7URAQZQY7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NRZQHJNXSREX7MK5P7URAQZQY7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NRZQHJNXSREX7MK5P7URAQZQY7","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":"d742dd797d0dc94bfb67abe6ddd074cb0b6d5a19a989e081698477ee96031c3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-10T23:28:00Z","title_canon_sha256":"bc6ba93f171fa5d7477990810e4c1cb6b1301d952c794ed76f825fbc42b374ef"},"schema_version":"1.0","source":{"id":"1610.03127","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03127","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03127v3","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03127","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"NRZQHJNXSREX","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NRZQHJNXSREX7MK5","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NRZQHJNX","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:cc8389b018513dc118672ecdb56ab4a4d1d45e69b52e8c60aee11ea1baae3c90","target":"graph","created_at":"2026-05-18T00:04:08Z","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 show that the category of $n$-excisive functors from the $\\infty$-category of spectra to a target stable $\\infty$-category $\\mathbf{E}$ is equivalent to the category of $\\mathbf{E}$-valued Mackey functors on an indexing category built from finite sets and surjections. This new classification of polynomial functors arises from an investigation of the structure present on cross effects. The path to this result involves a pair of surprising extension theorems for polynomial functors and a discussion of some interesting topics in semiadditive $\\infty$- category theory, including a formula for t","authors_text":"Saul Glasman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-10T23:28:00Z","title":"Goodwillie calculus and Mackey functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03127","kind":"arxiv","version":3},"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":"sha256:4a0dfda37c1137a63616fd08ec44be74c81ab13e7635708cf2cb67a8f777f771","target":"record","created_at":"2026-05-18T00:04:08Z","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":"d742dd797d0dc94bfb67abe6ddd074cb0b6d5a19a989e081698477ee96031c3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-10T23:28:00Z","title_canon_sha256":"bc6ba93f171fa5d7477990810e4c1cb6b1301d952c794ed76f825fbc42b374ef"},"schema_version":"1.0","source":{"id":"1610.03127","kind":"arxiv","version":3}},"canonical_sha256":"6c7303a5b794497fb15d7fe9104330c7e3e5a22c48bdc80b359b77111ec1a642","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c7303a5b794497fb15d7fe9104330c7e3e5a22c48bdc80b359b77111ec1a642","first_computed_at":"2026-05-18T00:04:08.539272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:08.539272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YLhxSXRxTETRPa9EM1/cOZP7RkGO7wBCk/wyu33wOHBCxEBLUr39tb3SYP77wcjL0HEXwmGKlQhgJ2ZATm6vAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:08.540001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03127","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a0dfda37c1137a63616fd08ec44be74c81ab13e7635708cf2cb67a8f777f771","sha256:cc8389b018513dc118672ecdb56ab4a4d1d45e69b52e8c60aee11ea1baae3c90"],"state_sha256":"72da7a5354cdeae18a0c74a8fe70891711852c67c01c5508ecb9f90d8f01d4c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m0sNxi8ZkbIn8wpRNA3UdXbYTRe+UPGMj0++IPeZijQTU6Lcw6I8mxdpdJ7lsusa+FeUDJ1bUd+tZHFaDIK1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:20:44.935040Z","bundle_sha256":"a33ebd9660a9b63107d298ad437bfba5c2a681658fabb859840b1d9a944e395b"}}