{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HNSHAMAM4WJ5NMWCZX2WG3RBF4","short_pith_number":"pith:HNSHAMAM","canonical_record":{"source":{"id":"1104.3657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-19T07:24:24Z","cross_cats_sorted":[],"title_canon_sha256":"064b13a78ed18b440c962031ef1b4cc966c398415f294f32d0996ac7490a3f9b","abstract_canon_sha256":"a0451425e740c8e53dfad796c697c5ed2e0388a88dd84b15d58ed087bdff9fcb"},"schema_version":"1.0"},"canonical_sha256":"3b6470300ce593d6b2c2cdf5636e212f2fbf7ced157f0ef88667aed07da4d791","source":{"kind":"arxiv","id":"1104.3657","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3657","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3657v1","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3657","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"pith_short_12","alias_value":"HNSHAMAM4WJ5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HNSHAMAM4WJ5NMWC","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HNSHAMAM","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HNSHAMAM4WJ5NMWCZX2WG3RBF4","target":"record","payload":{"canonical_record":{"source":{"id":"1104.3657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-19T07:24:24Z","cross_cats_sorted":[],"title_canon_sha256":"064b13a78ed18b440c962031ef1b4cc966c398415f294f32d0996ac7490a3f9b","abstract_canon_sha256":"a0451425e740c8e53dfad796c697c5ed2e0388a88dd84b15d58ed087bdff9fcb"},"schema_version":"1.0"},"canonical_sha256":"3b6470300ce593d6b2c2cdf5636e212f2fbf7ced157f0ef88667aed07da4d791","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:55.851026Z","signature_b64":"9JCAqfkj5ZEaOnqFyWk7rafwC2dOcCt3YbrNz8o+iUfgYhgXMV6uqBHRD/DBLnZBhi9mX4A1ipdmSkL64UZ1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b6470300ce593d6b2c2cdf5636e212f2fbf7ced157f0ef88667aed07da4d791","last_reissued_at":"2026-05-18T04:23:55.850655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:55.850655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.3657","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4dw4R5ttpAf98DpA/tmwlKrDBmGkCoFA9YW7n8e+YQAk2JKhSoF3EbpWlUoJZIrsRpxViP32Wbd1hGMgEOqLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T10:35:29.960199Z"},"content_sha256":"639d4ff9db82d8e6adf982fb163bfd80e3a68bf0b113d848572797adb82e8854","schema_version":"1.0","event_id":"sha256:639d4ff9db82d8e6adf982fb163bfd80e3a68bf0b113d848572797adb82e8854"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HNSHAMAM4WJ5NMWCZX2WG3RBF4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular Riemannian metrics, sub-rigidity vs rigidity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Abdelghani Zeghib (UMPA-ENSL), Samir Bekkara (USTO)","submitted_at":"2011-04-19T07:24:24Z","abstract_excerpt":"We analyze sub-Riemannian and lightlike metrics from the point of view of their rigidity as geometric structures. Following Cartan's and Gromov's formal definitions, they are never rigid, yet, in generic cases, they naturally give rise to rigid geometric structures!?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3657","kind":"arxiv","version":1},"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":"2026-05-18T04:23:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7bWK6lsiz/Nl92G/nNx+UPyezENgLBmTMUGUEh2HwLb2J4ovRJEG7FWe7rfYcAFFGSbH4a08hMpbQp2nZ0wjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T10:35:29.960755Z"},"content_sha256":"f8665e9c4cfc94c33e32ce3f59a234843e639b6367694bf7409c957681c2cf14","schema_version":"1.0","event_id":"sha256:f8665e9c4cfc94c33e32ce3f59a234843e639b6367694bf7409c957681c2cf14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNSHAMAM4WJ5NMWCZX2WG3RBF4/bundle.json","state_url":"https://pith.science/pith/HNSHAMAM4WJ5NMWCZX2WG3RBF4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNSHAMAM4WJ5NMWCZX2WG3RBF4/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":"2026-06-21T10:35:29Z","links":{"resolver":"https://pith.science/pith/HNSHAMAM4WJ5NMWCZX2WG3RBF4","bundle":"https://pith.science/pith/HNSHAMAM4WJ5NMWCZX2WG3RBF4/bundle.json","state":"https://pith.science/pith/HNSHAMAM4WJ5NMWCZX2WG3RBF4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNSHAMAM4WJ5NMWCZX2WG3RBF4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HNSHAMAM4WJ5NMWCZX2WG3RBF4","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":"a0451425e740c8e53dfad796c697c5ed2e0388a88dd84b15d58ed087bdff9fcb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-19T07:24:24Z","title_canon_sha256":"064b13a78ed18b440c962031ef1b4cc966c398415f294f32d0996ac7490a3f9b"},"schema_version":"1.0","source":{"id":"1104.3657","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3657","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3657v1","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3657","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"pith_short_12","alias_value":"HNSHAMAM4WJ5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HNSHAMAM4WJ5NMWC","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HNSHAMAM","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:f8665e9c4cfc94c33e32ce3f59a234843e639b6367694bf7409c957681c2cf14","target":"graph","created_at":"2026-05-18T04:23:55Z","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 analyze sub-Riemannian and lightlike metrics from the point of view of their rigidity as geometric structures. Following Cartan's and Gromov's formal definitions, they are never rigid, yet, in generic cases, they naturally give rise to rigid geometric structures!?","authors_text":"Abdelghani Zeghib (UMPA-ENSL), Samir Bekkara (USTO)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-19T07:24:24Z","title":"Singular Riemannian metrics, sub-rigidity vs rigidity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3657","kind":"arxiv","version":1},"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":"sha256:639d4ff9db82d8e6adf982fb163bfd80e3a68bf0b113d848572797adb82e8854","target":"record","created_at":"2026-05-18T04:23:55Z","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":"a0451425e740c8e53dfad796c697c5ed2e0388a88dd84b15d58ed087bdff9fcb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-19T07:24:24Z","title_canon_sha256":"064b13a78ed18b440c962031ef1b4cc966c398415f294f32d0996ac7490a3f9b"},"schema_version":"1.0","source":{"id":"1104.3657","kind":"arxiv","version":1}},"canonical_sha256":"3b6470300ce593d6b2c2cdf5636e212f2fbf7ced157f0ef88667aed07da4d791","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b6470300ce593d6b2c2cdf5636e212f2fbf7ced157f0ef88667aed07da4d791","first_computed_at":"2026-05-18T04:23:55.850655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:55.850655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9JCAqfkj5ZEaOnqFyWk7rafwC2dOcCt3YbrNz8o+iUfgYhgXMV6uqBHRD/DBLnZBhi9mX4A1ipdmSkL64UZ1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:55.851026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3657","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:639d4ff9db82d8e6adf982fb163bfd80e3a68bf0b113d848572797adb82e8854","sha256:f8665e9c4cfc94c33e32ce3f59a234843e639b6367694bf7409c957681c2cf14"],"state_sha256":"b416f6747692963aac506a66473279e726321a2d9131a2a4639fab6b8644c170"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LzHjfz8Brzvbx2ldAn9B+FTkV5RAIYHeOiQtdN8i/+vxCrEFVf7IYD/E2tiBTeiwbjPpJmmuaeIU3R4qYhLtCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T10:35:29.963302Z","bundle_sha256":"fcdd418de0aa6755e75f6f87b16e25a1e84b8f43bf5034a65ce4f02ee24c1451"}}