{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IZI7ZERG5V4ETDQZD6AGQCTL6P","short_pith_number":"pith:IZI7ZERG","canonical_record":{"source":{"id":"1712.04366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-12T16:00:08Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a9c20eef95d8e1e84392c013b3840814bd18e10da9437b2b08b726545913d94e","abstract_canon_sha256":"fa39a4d372ac3a5d5bb802cc3c81266a7113a9cd554c9203d351c196261878a6"},"schema_version":"1.0"},"canonical_sha256":"4651fc9226ed78498e191f80680a6bf3f84b54fe07980e36d26ab1a32e69bf9a","source":{"kind":"arxiv","id":"1712.04366","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04366","created_at":"2026-05-18T00:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04366v2","created_at":"2026-05-18T00:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04366","created_at":"2026-05-18T00:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"IZI7ZERG5V4E","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IZI7ZERG5V4ETDQZ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IZI7ZERG","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IZI7ZERG5V4ETDQZD6AGQCTL6P","target":"record","payload":{"canonical_record":{"source":{"id":"1712.04366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-12T16:00:08Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a9c20eef95d8e1e84392c013b3840814bd18e10da9437b2b08b726545913d94e","abstract_canon_sha256":"fa39a4d372ac3a5d5bb802cc3c81266a7113a9cd554c9203d351c196261878a6"},"schema_version":"1.0"},"canonical_sha256":"4651fc9226ed78498e191f80680a6bf3f84b54fe07980e36d26ab1a32e69bf9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:10.965078Z","signature_b64":"y/Tbvhr5xSMVGX/k3R8DcLtKrkTprhFzmmwRltTqh+h9Z9XugeNq8m45fGRKhmewJ/Xv6O52XKfqXOWLS12LCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4651fc9226ed78498e191f80680a6bf3f84b54fe07980e36d26ab1a32e69bf9a","last_reissued_at":"2026-05-18T00:10:10.964394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:10.964394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.04366","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":"2026-05-18T00:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3YC/6coYLkKEn7G/CnRuUkMcUHW0/Lee07u4zDxyl//B5J5BPGTDZ1vlQ0TYBEYrjUGMg1ETBetXkDeOUPm5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:17:59.113706Z"},"content_sha256":"6632654a7f13a3ff7ad990b484d46d207047bc0d6ca78688b6c87e0ffb46d7fe","schema_version":"1.0","event_id":"sha256:6632654a7f13a3ff7ad990b484d46d207047bc0d6ca78688b6c87e0ffb46d7fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IZI7ZERG5V4ETDQZD6AGQCTL6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The space of asymptotically conical self-expanders of mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jacob Bernstein, Lu Wang","submitted_at":"2017-12-12T16:00:08Z","abstract_excerpt":"We show that the space of asymptotically conical self-expanders of the mean curvature flow is a smooth Banach manifold. An immediate consequence is that non-degenerate self-expanders -- that is, those self-expanders that admit no non-trivial normal Jacobi fields that fix the asymptotic cone -- are generic in a certain sense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04366","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":"2026-05-18T00:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g5AmTLrfcHUVckAT4HxJvaQQdDlYC0fmd46P2G8xmQbjXNNkay/jSy5AcFTxcXJU0XzZRRtZjy7vJGuTh4QWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:17:59.114241Z"},"content_sha256":"f1bb255b7496bb9801df812d70792439e745274cb3f1b3c16e22d823dfa87fa3","schema_version":"1.0","event_id":"sha256:f1bb255b7496bb9801df812d70792439e745274cb3f1b3c16e22d823dfa87fa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IZI7ZERG5V4ETDQZD6AGQCTL6P/bundle.json","state_url":"https://pith.science/pith/IZI7ZERG5V4ETDQZD6AGQCTL6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IZI7ZERG5V4ETDQZD6AGQCTL6P/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":"2026-05-29T20:17:59Z","links":{"resolver":"https://pith.science/pith/IZI7ZERG5V4ETDQZD6AGQCTL6P","bundle":"https://pith.science/pith/IZI7ZERG5V4ETDQZD6AGQCTL6P/bundle.json","state":"https://pith.science/pith/IZI7ZERG5V4ETDQZD6AGQCTL6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IZI7ZERG5V4ETDQZD6AGQCTL6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IZI7ZERG5V4ETDQZD6AGQCTL6P","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":"fa39a4d372ac3a5d5bb802cc3c81266a7113a9cd554c9203d351c196261878a6","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-12T16:00:08Z","title_canon_sha256":"a9c20eef95d8e1e84392c013b3840814bd18e10da9437b2b08b726545913d94e"},"schema_version":"1.0","source":{"id":"1712.04366","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04366","created_at":"2026-05-18T00:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04366v2","created_at":"2026-05-18T00:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04366","created_at":"2026-05-18T00:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"IZI7ZERG5V4E","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IZI7ZERG5V4ETDQZ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IZI7ZERG","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:f1bb255b7496bb9801df812d70792439e745274cb3f1b3c16e22d823dfa87fa3","target":"graph","created_at":"2026-05-18T00:10:10Z","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 show that the space of asymptotically conical self-expanders of the mean curvature flow is a smooth Banach manifold. An immediate consequence is that non-degenerate self-expanders -- that is, those self-expanders that admit no non-trivial normal Jacobi fields that fix the asymptotic cone -- are generic in a certain sense.","authors_text":"Jacob Bernstein, Lu Wang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-12T16:00:08Z","title":"The space of asymptotically conical self-expanders of mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04366","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":"sha256:6632654a7f13a3ff7ad990b484d46d207047bc0d6ca78688b6c87e0ffb46d7fe","target":"record","created_at":"2026-05-18T00:10:10Z","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":"fa39a4d372ac3a5d5bb802cc3c81266a7113a9cd554c9203d351c196261878a6","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-12T16:00:08Z","title_canon_sha256":"a9c20eef95d8e1e84392c013b3840814bd18e10da9437b2b08b726545913d94e"},"schema_version":"1.0","source":{"id":"1712.04366","kind":"arxiv","version":2}},"canonical_sha256":"4651fc9226ed78498e191f80680a6bf3f84b54fe07980e36d26ab1a32e69bf9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4651fc9226ed78498e191f80680a6bf3f84b54fe07980e36d26ab1a32e69bf9a","first_computed_at":"2026-05-18T00:10:10.964394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:10.964394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y/Tbvhr5xSMVGX/k3R8DcLtKrkTprhFzmmwRltTqh+h9Z9XugeNq8m45fGRKhmewJ/Xv6O52XKfqXOWLS12LCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:10.965078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04366","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6632654a7f13a3ff7ad990b484d46d207047bc0d6ca78688b6c87e0ffb46d7fe","sha256:f1bb255b7496bb9801df812d70792439e745274cb3f1b3c16e22d823dfa87fa3"],"state_sha256":"ee36b50519138a917897ec64dbc5448c285165750af2d59ee3f89aa1b5963b2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tIaVRKyo5nSkje/U7i5kSczuZnCYy4gfNd6o+itUg7O/OkMUin+rHXCpOGaRR+zWadQjcX0yv1//TtA6m/0xCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:17:59.116764Z","bundle_sha256":"0fcb02d8098ac0640ef542f7e769537cd20a0b05a4200ae07d51c20da979559c"}}