{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:55ZG73WOCVH5TNBENMYLKUVCTE","short_pith_number":"pith:55ZG73WO","canonical_record":{"source":{"id":"0712.2533","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-12-17T16:26:59Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"4fddff12dca7b34416fda6445b599560307ff758eccd397a10515f74574aa3a2","abstract_canon_sha256":"65dc80fab1a0cb51df71ae7908fac05f171d2cd74f7c03225c16cdaebaf93fee"},"schema_version":"1.0"},"canonical_sha256":"ef726feece154fd9b4246b30b552a2993909390c6b3814dce3804635791ed0ff","source":{"kind":"arxiv","id":"0712.2533","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.2533","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"arxiv_version","alias_value":"0712.2533v3","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.2533","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"pith_short_12","alias_value":"55ZG73WOCVH5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"55ZG73WOCVH5TNBE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"55ZG73WO","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:55ZG73WOCVH5TNBENMYLKUVCTE","target":"record","payload":{"canonical_record":{"source":{"id":"0712.2533","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-12-17T16:26:59Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"4fddff12dca7b34416fda6445b599560307ff758eccd397a10515f74574aa3a2","abstract_canon_sha256":"65dc80fab1a0cb51df71ae7908fac05f171d2cd74f7c03225c16cdaebaf93fee"},"schema_version":"1.0"},"canonical_sha256":"ef726feece154fd9b4246b30b552a2993909390c6b3814dce3804635791ed0ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:06.429643Z","signature_b64":"fHmWNgUt8U3103VzOn9aSxuiAQ7whb9N047Xy0PgtA7np6s+Amr5K3lfDpH5NMT/fKdiICrqvfftU+26q/A+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef726feece154fd9b4246b30b552a2993909390c6b3814dce3804635791ed0ff","last_reissued_at":"2026-05-18T02:32:06.429257Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:06.429257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.2533","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":"2026-05-18T02:32:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63TA9WkRtr6tzACGC2vXDTpjhD/1WNYx8GlGMUNFw7RgM881pONwJeif7BZpZ1P4czKvLp9Su6SatVnMocv+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:45:37.545676Z"},"content_sha256":"f5ca5c14bc052962dc5f87aeba1801486767fe881985d57f22f985614926de7d","schema_version":"1.0","event_id":"sha256:f5ca5c14bc052962dc5f87aeba1801486767fe881985d57f22f985614926de7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:55ZG73WOCVH5TNBENMYLKUVCTE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Viterbo Transfer as a Map of Spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AT","authors_text":"Thomas Kragh","submitted_at":"2007-12-17T16:26:59Z","abstract_excerpt":"Let $L$ and $N$ be two smooth manifolds of the same dimension. Let $j\\colon L\\to T^*N$ be an exact Lagrange embedding. We denote the free loop space of $X$ by $\\Lambda X$. C. Viterbo constructed a transfer map $(\\Lambda j)^! \\colon H^*(\\Lambda L) \\to H^*(\\Lambda N)$. This transfer was constructed using finite dimensional approximation of Floer homology. In this paper we define a family of finite dimensional approximations and realize this transfer as a map of Thom spectra: $(\\Lambda j)_! \\colon (\\Lambda N)^{-TN} \\to (\\Lambda L)^{-TL+\\eta}$, where $\\eta$ is a virtual vector bundle classified by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.2533","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":"2026-05-18T02:32:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bcpn9G994tFV3oJPWQdrAAbt4J92hMOImn4F9vSyzhEWGC1Z3KLb0rsMjfvjv5d5JsJi8OgeYnezmNoiDLhKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:45:37.546364Z"},"content_sha256":"9f9a3219b3c90fce39a4d79aa418bdd085eb4a39721511e4718d31196abf85cb","schema_version":"1.0","event_id":"sha256:9f9a3219b3c90fce39a4d79aa418bdd085eb4a39721511e4718d31196abf85cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/55ZG73WOCVH5TNBENMYLKUVCTE/bundle.json","state_url":"https://pith.science/pith/55ZG73WOCVH5TNBENMYLKUVCTE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/55ZG73WOCVH5TNBENMYLKUVCTE/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":"2026-06-05T07:45:37Z","links":{"resolver":"https://pith.science/pith/55ZG73WOCVH5TNBENMYLKUVCTE","bundle":"https://pith.science/pith/55ZG73WOCVH5TNBENMYLKUVCTE/bundle.json","state":"https://pith.science/pith/55ZG73WOCVH5TNBENMYLKUVCTE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/55ZG73WOCVH5TNBENMYLKUVCTE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:55ZG73WOCVH5TNBENMYLKUVCTE","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":"65dc80fab1a0cb51df71ae7908fac05f171d2cd74f7c03225c16cdaebaf93fee","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-12-17T16:26:59Z","title_canon_sha256":"4fddff12dca7b34416fda6445b599560307ff758eccd397a10515f74574aa3a2"},"schema_version":"1.0","source":{"id":"0712.2533","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.2533","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"arxiv_version","alias_value":"0712.2533v3","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.2533","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"pith_short_12","alias_value":"55ZG73WOCVH5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"55ZG73WOCVH5TNBE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"55ZG73WO","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:9f9a3219b3c90fce39a4d79aa418bdd085eb4a39721511e4718d31196abf85cb","target":"graph","created_at":"2026-05-18T02:32:06Z","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":"Let $L$ and $N$ be two smooth manifolds of the same dimension. Let $j\\colon L\\to T^*N$ be an exact Lagrange embedding. We denote the free loop space of $X$ by $\\Lambda X$. C. Viterbo constructed a transfer map $(\\Lambda j)^! \\colon H^*(\\Lambda L) \\to H^*(\\Lambda N)$. This transfer was constructed using finite dimensional approximation of Floer homology. In this paper we define a family of finite dimensional approximations and realize this transfer as a map of Thom spectra: $(\\Lambda j)_! \\colon (\\Lambda N)^{-TN} \\to (\\Lambda L)^{-TL+\\eta}$, where $\\eta$ is a virtual vector bundle classified by","authors_text":"Thomas Kragh","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-12-17T16:26:59Z","title":"The Viterbo Transfer as a Map of Spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.2533","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:f5ca5c14bc052962dc5f87aeba1801486767fe881985d57f22f985614926de7d","target":"record","created_at":"2026-05-18T02:32:06Z","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":"65dc80fab1a0cb51df71ae7908fac05f171d2cd74f7c03225c16cdaebaf93fee","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-12-17T16:26:59Z","title_canon_sha256":"4fddff12dca7b34416fda6445b599560307ff758eccd397a10515f74574aa3a2"},"schema_version":"1.0","source":{"id":"0712.2533","kind":"arxiv","version":3}},"canonical_sha256":"ef726feece154fd9b4246b30b552a2993909390c6b3814dce3804635791ed0ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef726feece154fd9b4246b30b552a2993909390c6b3814dce3804635791ed0ff","first_computed_at":"2026-05-18T02:32:06.429257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:06.429257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fHmWNgUt8U3103VzOn9aSxuiAQ7whb9N047Xy0PgtA7np6s+Amr5K3lfDpH5NMT/fKdiICrqvfftU+26q/A+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:06.429643Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.2533","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5ca5c14bc052962dc5f87aeba1801486767fe881985d57f22f985614926de7d","sha256:9f9a3219b3c90fce39a4d79aa418bdd085eb4a39721511e4718d31196abf85cb"],"state_sha256":"c0e7e19567f291a94d483cec974b5d0c98c932e4b841d4a670acc587366cff93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XRcw9lld44EMagVrE+FtqJ6iS1ur4fhaWBcXyHQJ2d0btpb4RaAhilN5uUFmXHyMEmghbW3NPsdlekFlnhklCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T07:45:37.549604Z","bundle_sha256":"257dddd0bd0de40ef2a688582430032550e5d9947609b82e1f3daa7aa55d18bd"}}