{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DCTW3ABRVVNWSJTK5HEQXTM366","short_pith_number":"pith:DCTW3ABR","canonical_record":{"source":{"id":"1103.5511","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-28T23:52:45Z","cross_cats_sorted":[],"title_canon_sha256":"a9d1b776a036ed6864b13ffc9f2bc6d05bf20ae6479a2fac68c3ebe3fc93af7d","abstract_canon_sha256":"704be62c9b3e6346bcfcf03e38b7554c0362e9286732c137c097233360c79d2b"},"schema_version":"1.0"},"canonical_sha256":"18a76d8031ad5b69266ae9c90bcd9bf7ab9443a71c5c2326db5384e4df5fb5da","source":{"kind":"arxiv","id":"1103.5511","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5511","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5511v2","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5511","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"DCTW3ABRVVNW","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DCTW3ABRVVNWSJTK","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DCTW3ABR","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DCTW3ABRVVNWSJTK5HEQXTM366","target":"record","payload":{"canonical_record":{"source":{"id":"1103.5511","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-28T23:52:45Z","cross_cats_sorted":[],"title_canon_sha256":"a9d1b776a036ed6864b13ffc9f2bc6d05bf20ae6479a2fac68c3ebe3fc93af7d","abstract_canon_sha256":"704be62c9b3e6346bcfcf03e38b7554c0362e9286732c137c097233360c79d2b"},"schema_version":"1.0"},"canonical_sha256":"18a76d8031ad5b69266ae9c90bcd9bf7ab9443a71c5c2326db5384e4df5fb5da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:36.663815Z","signature_b64":"cSuSL+617RZuPccEXm0MUzDWOZJWTNKOl4xy0tLrmzyC126uz7Npkj2uiXOCEONkp5PQRA1Nfes4vS8LQT/KDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18a76d8031ad5b69266ae9c90bcd9bf7ab9443a71c5c2326db5384e4df5fb5da","last_reissued_at":"2026-05-17T23:53:36.663260Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:36.663260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.5511","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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ZrPX2Kc5O47zuA7ni+Vo9T+leR1BQizI5ZomARSHgfaKYLjQno+1Lqi2YKz/G18ZhmfZpkfEn31Hoh3ELNHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T03:17:01.355059Z"},"content_sha256":"9e83d7c71f33fd36a6c39e972bd2dbb85658d15426e2b15205f2268d7c8ba9b9","schema_version":"1.0","event_id":"sha256:9e83d7c71f33fd36a6c39e972bd2dbb85658d15426e2b15205f2268d7c8ba9b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DCTW3ABRVVNWSJTK5HEQXTM366","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scattering rigidity with trapped geodesics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Christopher B. Croke","submitted_at":"2011-03-28T23:52:45Z","abstract_excerpt":"We prove that the flat product metric on $D^n\\times S^1$ is scattering rigid where $D^n$ is the unit ball in $\\R^n$ and $n\\geq 2$. The scattering data (loosely speaking) of a Riemannian manifold with boundary is map $S:U^+\\partial M\\to U^-\\partial M$ from unit vectors $V$ at the boundary that point inward to unit vectors at the boundary that point outwards. The map (where defined) takes $V$ to $\\gamma'_V(T_0)$ where $\\gamma_V$ is the unit speed geodesic determined by $V$ and $T_0$ is the first positive value of $t$ (when it exists) such that $\\gamma_V(t)$ again lies in the boundary. We show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5511","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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OaQ2DOHvmXQ69+THmxCWZEjRuQodw93/JP3QlORcyznnzyftKD8rBbSHDGGftnsmZ6Nd+bbPPUaARrRKGTiQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T03:17:01.355440Z"},"content_sha256":"0ff4777838eefd05dd1f3578f5a00570595eee430dc0e341a1a2c88f3e7667fd","schema_version":"1.0","event_id":"sha256:0ff4777838eefd05dd1f3578f5a00570595eee430dc0e341a1a2c88f3e7667fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DCTW3ABRVVNWSJTK5HEQXTM366/bundle.json","state_url":"https://pith.science/pith/DCTW3ABRVVNWSJTK5HEQXTM366/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DCTW3ABRVVNWSJTK5HEQXTM366/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":"2026-07-02T03:17:01Z","links":{"resolver":"https://pith.science/pith/DCTW3ABRVVNWSJTK5HEQXTM366","bundle":"https://pith.science/pith/DCTW3ABRVVNWSJTK5HEQXTM366/bundle.json","state":"https://pith.science/pith/DCTW3ABRVVNWSJTK5HEQXTM366/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DCTW3ABRVVNWSJTK5HEQXTM366/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DCTW3ABRVVNWSJTK5HEQXTM366","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":"704be62c9b3e6346bcfcf03e38b7554c0362e9286732c137c097233360c79d2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-28T23:52:45Z","title_canon_sha256":"a9d1b776a036ed6864b13ffc9f2bc6d05bf20ae6479a2fac68c3ebe3fc93af7d"},"schema_version":"1.0","source":{"id":"1103.5511","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5511","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5511v2","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5511","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"DCTW3ABRVVNW","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DCTW3ABRVVNWSJTK","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DCTW3ABR","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:0ff4777838eefd05dd1f3578f5a00570595eee430dc0e341a1a2c88f3e7667fd","target":"graph","created_at":"2026-05-17T23:53:36Z","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 prove that the flat product metric on $D^n\\times S^1$ is scattering rigid where $D^n$ is the unit ball in $\\R^n$ and $n\\geq 2$. The scattering data (loosely speaking) of a Riemannian manifold with boundary is map $S:U^+\\partial M\\to U^-\\partial M$ from unit vectors $V$ at the boundary that point inward to unit vectors at the boundary that point outwards. The map (where defined) takes $V$ to $\\gamma'_V(T_0)$ where $\\gamma_V$ is the unit speed geodesic determined by $V$ and $T_0$ is the first positive value of $t$ (when it exists) such that $\\gamma_V(t)$ again lies in the boundary. We show th","authors_text":"Christopher B. Croke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-28T23:52:45Z","title":"Scattering rigidity with trapped geodesics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5511","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":"sha256:9e83d7c71f33fd36a6c39e972bd2dbb85658d15426e2b15205f2268d7c8ba9b9","target":"record","created_at":"2026-05-17T23:53:36Z","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":"704be62c9b3e6346bcfcf03e38b7554c0362e9286732c137c097233360c79d2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-28T23:52:45Z","title_canon_sha256":"a9d1b776a036ed6864b13ffc9f2bc6d05bf20ae6479a2fac68c3ebe3fc93af7d"},"schema_version":"1.0","source":{"id":"1103.5511","kind":"arxiv","version":2}},"canonical_sha256":"18a76d8031ad5b69266ae9c90bcd9bf7ab9443a71c5c2326db5384e4df5fb5da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18a76d8031ad5b69266ae9c90bcd9bf7ab9443a71c5c2326db5384e4df5fb5da","first_computed_at":"2026-05-17T23:53:36.663260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.663260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cSuSL+617RZuPccEXm0MUzDWOZJWTNKOl4xy0tLrmzyC126uz7Npkj2uiXOCEONkp5PQRA1Nfes4vS8LQT/KDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.663815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.5511","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e83d7c71f33fd36a6c39e972bd2dbb85658d15426e2b15205f2268d7c8ba9b9","sha256:0ff4777838eefd05dd1f3578f5a00570595eee430dc0e341a1a2c88f3e7667fd"],"state_sha256":"bfe844fbcbf33bd53cea3e0ff9a55c1ee2899497d0320382e5910e0864c87eca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/d0qflFMWw+7hMdm3s9R7/RXZEpCOE43GkN0ycLO9NKQQZE97PoJSy0BbdSmMaUh8woIGnxUlfM7kFvNQdq/Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T03:17:01.357835Z","bundle_sha256":"d0206b17425853ba2bc8e199f777fd93b7b086a50c2bdedd9ea184dca57250fb"}}