{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:MGLTHHJCI5XRHF3JEYWTXWGT7E","short_pith_number":"pith:MGLTHHJC","canonical_record":{"source":{"id":"math/0605668","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2006-05-25T20:29:51Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"2730e244410a55bd0baab1db36b7a8cf011119ec744199e9f896d827bf2befa3","abstract_canon_sha256":"e091be7528f5fdf2578252315631988d0a7706752d96c0e5467431cd5d969936"},"schema_version":"1.0"},"canonical_sha256":"6197339d22476f139769262d3bd8d3f908815a36bc2631ee6db7240a16c5f33d","source":{"kind":"arxiv","id":"math/0605668","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605668","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605668v2","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605668","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"MGLTHHJCI5XR","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"MGLTHHJCI5XRHF3J","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"MGLTHHJC","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:MGLTHHJCI5XRHF3JEYWTXWGT7E","target":"record","payload":{"canonical_record":{"source":{"id":"math/0605668","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2006-05-25T20:29:51Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"2730e244410a55bd0baab1db36b7a8cf011119ec744199e9f896d827bf2befa3","abstract_canon_sha256":"e091be7528f5fdf2578252315631988d0a7706752d96c0e5467431cd5d969936"},"schema_version":"1.0"},"canonical_sha256":"6197339d22476f139769262d3bd8d3f908815a36bc2631ee6db7240a16c5f33d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:47.994531Z","signature_b64":"nz5JoMB2py+AExipDdb9HVpHpiUTsqcnoOoxdTp+lr8iUmC7UgShw6psTh5c5ZuWrjMLCZyPfa2hMpc01wnYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6197339d22476f139769262d3bd8d3f908815a36bc2631ee6db7240a16c5f33d","last_reissued_at":"2026-05-18T04:35:47.994086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:47.994086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0605668","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":"2026-05-18T04:35:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJWf+qtoMPyxhqYwQZ6UAP91PSF0/l0yQz7LcOyfBAnphz58HWArP0Mh7lx899Q4m+9w3gBcAY2FhVTU4etzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T17:18:00.158265Z"},"content_sha256":"209800c740f26ccae474c21de8b2e5adb7d5fc030c459ba10c09b945ce79fa07","schema_version":"1.0","event_id":"sha256:209800c740f26ccae474c21de8b2e5adb7d5fc030c459ba10c09b945ce79fa07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:MGLTHHJCI5XRHF3JEYWTXWGT7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distortion Minimal Morphing I: The Theory For Stretching","license":"","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DG","authors_text":"Carmen Chicone, Oksana Bihun","submitted_at":"2006-05-25T20:29:51Z","abstract_excerpt":"We consider the problem of distortion minimal morphing of $n$-dimensional compact connected oriented smooth manifolds without boundary embedded in $\\R^{n+1}$. Distortion involves bending and stretching. In this paper, minimal distortion (with respect to stretching) is defined as the infinitesimal relative change in volume. The existence of minimal distortion diffeomorphisms between diffeomorphic manifolds is proved. A definition of minimal distortion morphing between two isotopic manifolds is given, and the existence of minimal distortion morphs between every pair of isotopic embedded manifold"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605668","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":"2026-05-18T04:35:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Xw64yhCpqNrcTSMJrENSGreSSHCH2QnrXEyhHh9mtQpP8C680DtpCxP7TRmgMdMk1j9sagy9UbjUH3GZGa0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T17:18:00.158979Z"},"content_sha256":"5dfbae14726b437cfe940fcab6048bc6600518b321d28e1296480a449c481f4b","schema_version":"1.0","event_id":"sha256:5dfbae14726b437cfe940fcab6048bc6600518b321d28e1296480a449c481f4b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGLTHHJCI5XRHF3JEYWTXWGT7E/bundle.json","state_url":"https://pith.science/pith/MGLTHHJCI5XRHF3JEYWTXWGT7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGLTHHJCI5XRHF3JEYWTXWGT7E/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":"2026-05-24T17:18:00Z","links":{"resolver":"https://pith.science/pith/MGLTHHJCI5XRHF3JEYWTXWGT7E","bundle":"https://pith.science/pith/MGLTHHJCI5XRHF3JEYWTXWGT7E/bundle.json","state":"https://pith.science/pith/MGLTHHJCI5XRHF3JEYWTXWGT7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGLTHHJCI5XRHF3JEYWTXWGT7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:MGLTHHJCI5XRHF3JEYWTXWGT7E","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":"e091be7528f5fdf2578252315631988d0a7706752d96c0e5467431cd5d969936","cross_cats_sorted":["math.OC"],"license":"","primary_cat":"math.DG","submitted_at":"2006-05-25T20:29:51Z","title_canon_sha256":"2730e244410a55bd0baab1db36b7a8cf011119ec744199e9f896d827bf2befa3"},"schema_version":"1.0","source":{"id":"math/0605668","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605668","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605668v2","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605668","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"MGLTHHJCI5XR","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"MGLTHHJCI5XRHF3J","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"MGLTHHJC","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:5dfbae14726b437cfe940fcab6048bc6600518b321d28e1296480a449c481f4b","target":"graph","created_at":"2026-05-18T04:35:47Z","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 consider the problem of distortion minimal morphing of $n$-dimensional compact connected oriented smooth manifolds without boundary embedded in $\\R^{n+1}$. Distortion involves bending and stretching. In this paper, minimal distortion (with respect to stretching) is defined as the infinitesimal relative change in volume. The existence of minimal distortion diffeomorphisms between diffeomorphic manifolds is proved. A definition of minimal distortion morphing between two isotopic manifolds is given, and the existence of minimal distortion morphs between every pair of isotopic embedded manifold","authors_text":"Carmen Chicone, Oksana Bihun","cross_cats":["math.OC"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2006-05-25T20:29:51Z","title":"Distortion Minimal Morphing I: The Theory For Stretching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605668","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":"sha256:209800c740f26ccae474c21de8b2e5adb7d5fc030c459ba10c09b945ce79fa07","target":"record","created_at":"2026-05-18T04:35:47Z","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":"e091be7528f5fdf2578252315631988d0a7706752d96c0e5467431cd5d969936","cross_cats_sorted":["math.OC"],"license":"","primary_cat":"math.DG","submitted_at":"2006-05-25T20:29:51Z","title_canon_sha256":"2730e244410a55bd0baab1db36b7a8cf011119ec744199e9f896d827bf2befa3"},"schema_version":"1.0","source":{"id":"math/0605668","kind":"arxiv","version":2}},"canonical_sha256":"6197339d22476f139769262d3bd8d3f908815a36bc2631ee6db7240a16c5f33d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6197339d22476f139769262d3bd8d3f908815a36bc2631ee6db7240a16c5f33d","first_computed_at":"2026-05-18T04:35:47.994086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:47.994086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nz5JoMB2py+AExipDdb9HVpHpiUTsqcnoOoxdTp+lr8iUmC7UgShw6psTh5c5ZuWrjMLCZyPfa2hMpc01wnYDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:47.994531Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605668","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:209800c740f26ccae474c21de8b2e5adb7d5fc030c459ba10c09b945ce79fa07","sha256:5dfbae14726b437cfe940fcab6048bc6600518b321d28e1296480a449c481f4b"],"state_sha256":"7d1394d339175aee8eb8279d87c642fcbb07ef8d9cde6704a3cce8052a5891ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P83bQEfOel3PYgpzuOCPntbrlSGYTCqnO5sk77chh0O2Scj5AsZQDkyfz8yUOBCgHW/3UJF9msblKmHqE3xADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T17:18:00.161938Z","bundle_sha256":"3935d2eddb1fde58286c664025d9b0c83109c985b7174b0851ce46005ce0fe43"}}