{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:ZL5N3ZSY4TIZTYULPZZFVGLXSV","short_pith_number":"pith:ZL5N3ZSY","canonical_record":{"source":{"id":"0707.3489","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2007-07-24T08:09:05Z","cross_cats_sorted":[],"title_canon_sha256":"75217d2a364fef160e80c43b77b0bfa9e5ed29bdeb973909d26925ff80166cc1","abstract_canon_sha256":"2ef7caec09a95b01da11c1aa6325a444b126fb8d3edf14befecacd6fd6cb1f45"},"schema_version":"1.0"},"canonical_sha256":"cafadde658e4d199e28b7e725a9977957c538a3a97b6eb825399e61a43a41b00","source":{"kind":"arxiv","id":"0707.3489","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.3489","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"arxiv_version","alias_value":"0707.3489v2","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.3489","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZL5N3ZSY4TIZ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ZL5N3ZSY4TIZTYUL","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ZL5N3ZSY","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:ZL5N3ZSY4TIZTYULPZZFVGLXSV","target":"record","payload":{"canonical_record":{"source":{"id":"0707.3489","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2007-07-24T08:09:05Z","cross_cats_sorted":[],"title_canon_sha256":"75217d2a364fef160e80c43b77b0bfa9e5ed29bdeb973909d26925ff80166cc1","abstract_canon_sha256":"2ef7caec09a95b01da11c1aa6325a444b126fb8d3edf14befecacd6fd6cb1f45"},"schema_version":"1.0"},"canonical_sha256":"cafadde658e4d199e28b7e725a9977957c538a3a97b6eb825399e61a43a41b00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:12.529381Z","signature_b64":"xlHGuRjPUtW739McjxxcZwNVM9S9Bb9XHdEinEMZ2W5zdfRb1dF3VGgW5WrqJn2Oygjs2TQzQP5kfCEOZ87DBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cafadde658e4d199e28b7e725a9977957c538a3a97b6eb825399e61a43a41b00","last_reissued_at":"2026-05-18T02:58:12.528504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:12.528504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.3489","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":"2026-05-18T02:58:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jSNlkZXrhr163t9tuB+7SiRiSVCQBE2TYIo0zsMhmg85dAjmDigRPwzzsamcgoUvq45FHFQqYZ6RrDTvkGaHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:30:27.000821Z"},"content_sha256":"0f7cf21b53c1b71804a1236f0a77aac3b6d8751373e32ce71d34f92ab5413892","schema_version":"1.0","event_id":"sha256:0f7cf21b53c1b71804a1236f0a77aac3b6d8751373e32ce71d34f92ab5413892"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:ZL5N3ZSY4TIZTYULPZZFVGLXSV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivatives of embedding functors I: the stable case","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Gregory Arone","submitted_at":"2007-07-24T08:09:05Z","abstract_excerpt":"For smooth manifolds $M$ and $N$, let $\\Ebar(M, N)$ be the homotopy fiber of the map $\\Emb(M, N)\\longrightarrow \\Imm(M, N)$. Consider the functor from the category of Euclidean spaces to the category of spectra, defined by the formula $V\\mapsto \\Sigma^\\infty\\Ebar(M, N\\times V)$. In this paper, we describe the Taylor polynomials of this functor, in the sense of M. Weiss' orthogonal calculus, in the case when $N$ is a nice open submanifold of a Euclidean space. This leads to a description of the derivatives of this functor when $N$ is a tame stably parallelizable manifold (we believe that the pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3489","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":"2026-05-18T02:58:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yN95e3gEGLml0VK0TO5EdFVE18qpzNcxnV/DawRNn7gKBi6EKPGTqqqNmLfd2clnLC3s/+Sl6okeENFY0tkjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:30:27.001149Z"},"content_sha256":"10eb5f6e66c70f01ac3dbe90d0d93f91fe126da1ce693c96bd137386804f3fc0","schema_version":"1.0","event_id":"sha256:10eb5f6e66c70f01ac3dbe90d0d93f91fe126da1ce693c96bd137386804f3fc0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZL5N3ZSY4TIZTYULPZZFVGLXSV/bundle.json","state_url":"https://pith.science/pith/ZL5N3ZSY4TIZTYULPZZFVGLXSV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZL5N3ZSY4TIZTYULPZZFVGLXSV/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":"2026-06-24T17:30:27Z","links":{"resolver":"https://pith.science/pith/ZL5N3ZSY4TIZTYULPZZFVGLXSV","bundle":"https://pith.science/pith/ZL5N3ZSY4TIZTYULPZZFVGLXSV/bundle.json","state":"https://pith.science/pith/ZL5N3ZSY4TIZTYULPZZFVGLXSV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZL5N3ZSY4TIZTYULPZZFVGLXSV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ZL5N3ZSY4TIZTYULPZZFVGLXSV","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":"2ef7caec09a95b01da11c1aa6325a444b126fb8d3edf14befecacd6fd6cb1f45","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2007-07-24T08:09:05Z","title_canon_sha256":"75217d2a364fef160e80c43b77b0bfa9e5ed29bdeb973909d26925ff80166cc1"},"schema_version":"1.0","source":{"id":"0707.3489","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.3489","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"arxiv_version","alias_value":"0707.3489v2","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.3489","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZL5N3ZSY4TIZ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ZL5N3ZSY4TIZTYUL","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ZL5N3ZSY","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:10eb5f6e66c70f01ac3dbe90d0d93f91fe126da1ce693c96bd137386804f3fc0","target":"graph","created_at":"2026-05-18T02:58:12Z","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":"For smooth manifolds $M$ and $N$, let $\\Ebar(M, N)$ be the homotopy fiber of the map $\\Emb(M, N)\\longrightarrow \\Imm(M, N)$. Consider the functor from the category of Euclidean spaces to the category of spectra, defined by the formula $V\\mapsto \\Sigma^\\infty\\Ebar(M, N\\times V)$. In this paper, we describe the Taylor polynomials of this functor, in the sense of M. Weiss' orthogonal calculus, in the case when $N$ is a nice open submanifold of a Euclidean space. This leads to a description of the derivatives of this functor when $N$ is a tame stably parallelizable manifold (we believe that the pa","authors_text":"Gregory Arone","cross_cats":[],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2007-07-24T08:09:05Z","title":"Derivatives of embedding functors I: the stable case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3489","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":"sha256:0f7cf21b53c1b71804a1236f0a77aac3b6d8751373e32ce71d34f92ab5413892","target":"record","created_at":"2026-05-18T02:58:12Z","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":"2ef7caec09a95b01da11c1aa6325a444b126fb8d3edf14befecacd6fd6cb1f45","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2007-07-24T08:09:05Z","title_canon_sha256":"75217d2a364fef160e80c43b77b0bfa9e5ed29bdeb973909d26925ff80166cc1"},"schema_version":"1.0","source":{"id":"0707.3489","kind":"arxiv","version":2}},"canonical_sha256":"cafadde658e4d199e28b7e725a9977957c538a3a97b6eb825399e61a43a41b00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cafadde658e4d199e28b7e725a9977957c538a3a97b6eb825399e61a43a41b00","first_computed_at":"2026-05-18T02:58:12.528504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:12.528504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xlHGuRjPUtW739McjxxcZwNVM9S9Bb9XHdEinEMZ2W5zdfRb1dF3VGgW5WrqJn2Oygjs2TQzQP5kfCEOZ87DBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:12.529381Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.3489","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f7cf21b53c1b71804a1236f0a77aac3b6d8751373e32ce71d34f92ab5413892","sha256:10eb5f6e66c70f01ac3dbe90d0d93f91fe126da1ce693c96bd137386804f3fc0"],"state_sha256":"fd52ab4576748b2210b36964aa694c54210bf77e60643e158a3dbec284c806c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"16le4ow1Y6MIJJmnTFfbTEfUpaIHnDkUOEayMyaUgyeUOfdOdyk6abWPV1rAyc5uoJYpSj0wUz8ZuNdaurcHBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T17:30:27.003175Z","bundle_sha256":"b80c113fbdd7d7167bf51fa748174bc82049cd9ca7b43735c669085a3282d924"}}