{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2UTHOJGN7EZDDV3Q42D4NSTXW5","short_pith_number":"pith:2UTHOJGN","canonical_record":{"source":{"id":"1605.02128","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-05-07T01:39:43Z","cross_cats_sorted":[],"title_canon_sha256":"8dd04798e1379d758aa54a1784d0cb1d5339f024af759d077ef1612a89719261","abstract_canon_sha256":"44d6b109b9cab071f84d136dc383806ddc24ff4282dddc8aeef00af7245ce4f3"},"schema_version":"1.0"},"canonical_sha256":"d5267724cdf93231d770e687c6ca77b76f75acb10c048be5237fdb33cf592df0","source":{"kind":"arxiv","id":"1605.02128","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02128","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02128v2","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02128","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"2UTHOJGN7EZD","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2UTHOJGN7EZDDV3Q","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2UTHOJGN","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2UTHOJGN7EZDDV3Q42D4NSTXW5","target":"record","payload":{"canonical_record":{"source":{"id":"1605.02128","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-05-07T01:39:43Z","cross_cats_sorted":[],"title_canon_sha256":"8dd04798e1379d758aa54a1784d0cb1d5339f024af759d077ef1612a89719261","abstract_canon_sha256":"44d6b109b9cab071f84d136dc383806ddc24ff4282dddc8aeef00af7245ce4f3"},"schema_version":"1.0"},"canonical_sha256":"d5267724cdf93231d770e687c6ca77b76f75acb10c048be5237fdb33cf592df0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:39.201140Z","signature_b64":"SW8VqHCMR8uDCI6XUR8FbTtpcEhYnD+HnSWV21Lnnw2x0sGNEbIjLB2Mhm2pPHRRCOEAENSQJ088kIbWS7K+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5267724cdf93231d770e687c6ca77b76f75acb10c048be5237fdb33cf592df0","last_reissued_at":"2026-05-18T00:55:39.200492Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:39.200492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.02128","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":"2026-05-18T00:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ko0s4rszirdlTIqqJ7tMPOkfBZB/9mX1iGGwlMKHiMNo3vg5hAroO8g7a3MU+IR4oBpAzTSjSaoOzwleoxTGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:53:56.303640Z"},"content_sha256":"313dafcc3dc060b708c27c77456f072c1496d2a6f13f28d2ee90e399cbb49643","schema_version":"1.0","event_id":"sha256:313dafcc3dc060b708c27c77456f072c1496d2a6f13f28d2ee90e399cbb49643"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2UTHOJGN7EZDDV3Q42D4NSTXW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Note on asymptotically conical expanding Ricci solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"John Lott, Patrick Wilson","submitted_at":"2016-05-07T01:39:43Z","abstract_excerpt":"We show that at the level of formal expansions, any compact Riemannian manifold is the sphere at infinity of an asymptotically conical gradient expanding Ricci soliton."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02128","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":"2026-05-18T00:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dSOdUslzPFzFq6iGow8MI9P+4BkAl4MMuguHyPQJ+czfuRTs9GSWS0lLpU0qVHtCOG4TOR+gwF3wnGB2tTzJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:53:56.304021Z"},"content_sha256":"b0750085248a9d561cd49b871161bdb76c7bd6b25ca5502b12f03c164227e156","schema_version":"1.0","event_id":"sha256:b0750085248a9d561cd49b871161bdb76c7bd6b25ca5502b12f03c164227e156"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2UTHOJGN7EZDDV3Q42D4NSTXW5/bundle.json","state_url":"https://pith.science/pith/2UTHOJGN7EZDDV3Q42D4NSTXW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2UTHOJGN7EZDDV3Q42D4NSTXW5/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":"2026-06-05T08:53:56Z","links":{"resolver":"https://pith.science/pith/2UTHOJGN7EZDDV3Q42D4NSTXW5","bundle":"https://pith.science/pith/2UTHOJGN7EZDDV3Q42D4NSTXW5/bundle.json","state":"https://pith.science/pith/2UTHOJGN7EZDDV3Q42D4NSTXW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2UTHOJGN7EZDDV3Q42D4NSTXW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2UTHOJGN7EZDDV3Q42D4NSTXW5","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":"44d6b109b9cab071f84d136dc383806ddc24ff4282dddc8aeef00af7245ce4f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-05-07T01:39:43Z","title_canon_sha256":"8dd04798e1379d758aa54a1784d0cb1d5339f024af759d077ef1612a89719261"},"schema_version":"1.0","source":{"id":"1605.02128","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02128","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02128v2","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02128","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"2UTHOJGN7EZD","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2UTHOJGN7EZDDV3Q","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2UTHOJGN","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:b0750085248a9d561cd49b871161bdb76c7bd6b25ca5502b12f03c164227e156","target":"graph","created_at":"2026-05-18T00:55:39Z","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 at the level of formal expansions, any compact Riemannian manifold is the sphere at infinity of an asymptotically conical gradient expanding Ricci soliton.","authors_text":"John Lott, Patrick Wilson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-05-07T01:39:43Z","title":"Note on asymptotically conical expanding Ricci solitons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02128","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":"sha256:313dafcc3dc060b708c27c77456f072c1496d2a6f13f28d2ee90e399cbb49643","target":"record","created_at":"2026-05-18T00:55:39Z","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":"44d6b109b9cab071f84d136dc383806ddc24ff4282dddc8aeef00af7245ce4f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-05-07T01:39:43Z","title_canon_sha256":"8dd04798e1379d758aa54a1784d0cb1d5339f024af759d077ef1612a89719261"},"schema_version":"1.0","source":{"id":"1605.02128","kind":"arxiv","version":2}},"canonical_sha256":"d5267724cdf93231d770e687c6ca77b76f75acb10c048be5237fdb33cf592df0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5267724cdf93231d770e687c6ca77b76f75acb10c048be5237fdb33cf592df0","first_computed_at":"2026-05-18T00:55:39.200492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:39.200492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SW8VqHCMR8uDCI6XUR8FbTtpcEhYnD+HnSWV21Lnnw2x0sGNEbIjLB2Mhm2pPHRRCOEAENSQJ088kIbWS7K+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:39.201140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02128","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:313dafcc3dc060b708c27c77456f072c1496d2a6f13f28d2ee90e399cbb49643","sha256:b0750085248a9d561cd49b871161bdb76c7bd6b25ca5502b12f03c164227e156"],"state_sha256":"3a6f857a37a79b80a5fe288739c41e70dd1133cde972cc58cfd7ecbf994398eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ayyyHdhw439hqz9aY9yxcaMLhOAgtkvt6sYgV7cJGohHHksTPb5+tDyvLzec1jIrvxiiMRHG1M8RrFsHjVDDAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:53:56.306414Z","bundle_sha256":"2db6c8fe43af483a1f2537d388bee4c73754e0fbef5f94acfc5c99d3fdda2708"}}