{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QEKJ57H4QITV3FQDI235DUVLJ6","short_pith_number":"pith:QEKJ57H4","canonical_record":{"source":{"id":"1210.4102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-15T16:55:30Z","cross_cats_sorted":[],"title_canon_sha256":"c549c32c3c6ed7e2c3db3b76c08246f0e59d236090b9cdee16653ae15e7b725a","abstract_canon_sha256":"fce6470e9baf85ec495ca6ad04630422a91b4f18aca331f42668b76caa063747"},"schema_version":"1.0"},"canonical_sha256":"81149efcfc82275d960346b7d1d2ab4fa4b20a89ef63a5a0ababe95517c09275","source":{"kind":"arxiv","id":"1210.4102","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4102","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4102v1","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4102","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"pith_short_12","alias_value":"QEKJ57H4QITV","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QEKJ57H4QITV3FQD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QEKJ57H4","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QEKJ57H4QITV3FQDI235DUVLJ6","target":"record","payload":{"canonical_record":{"source":{"id":"1210.4102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-15T16:55:30Z","cross_cats_sorted":[],"title_canon_sha256":"c549c32c3c6ed7e2c3db3b76c08246f0e59d236090b9cdee16653ae15e7b725a","abstract_canon_sha256":"fce6470e9baf85ec495ca6ad04630422a91b4f18aca331f42668b76caa063747"},"schema_version":"1.0"},"canonical_sha256":"81149efcfc82275d960346b7d1d2ab4fa4b20a89ef63a5a0ababe95517c09275","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:07.997084Z","signature_b64":"r6kIG4Gm0JRtm5wd/U9ol6OoA/V7nNJnkG6Ttqf7/v1OyPLO/CcZk/Zdp4gFKUvpFp3SX3jZSNuWmfVRnkQcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81149efcfc82275d960346b7d1d2ab4fa4b20a89ef63a5a0ababe95517c09275","last_reissued_at":"2026-05-18T03:43:07.996362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:07.996362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.4102","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":"2026-05-18T03:43:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bd2ZLM3R5OYIBXm2l6EuoKr3Tng0zUcfVVeNumGDkPuZPWkuezXgjtPW0L3/upzvQkoeEQIdq1YEsgs/abubDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:38:09.673042Z"},"content_sha256":"f559066b9ab8ce16f12b80c600c40407bad1825b1620712c0e8b12cc2f78045f","schema_version":"1.0","event_id":"sha256:f559066b9ab8ce16f12b80c600c40407bad1825b1620712c0e8b12cc2f78045f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QEKJ57H4QITV3FQDI235DUVLJ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riemannian Manifolds with positive sectional curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Wolfgang Ziller","submitted_at":"2012-10-15T16:55:30Z","abstract_excerpt":"This is a survey of recent results on manifolds with positive curvature from a series of lecture given in Guanajuato, Mexico in 2010. It also contains some hitsorical comments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4102","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":"2026-05-18T03:43:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ii1nSNeQdS04dEk/ZPaBL3txTBYefhv9b8a0g42LoUoTq0NZq4+j16ELTlGcZ6roXJuSGrBH3DaKdbu/eD/LDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:38:09.673400Z"},"content_sha256":"166b40611e4e4c6621df6115cf1bc3b1757c7cf9e21fd0821e314a74f8396ebf","schema_version":"1.0","event_id":"sha256:166b40611e4e4c6621df6115cf1bc3b1757c7cf9e21fd0821e314a74f8396ebf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QEKJ57H4QITV3FQDI235DUVLJ6/bundle.json","state_url":"https://pith.science/pith/QEKJ57H4QITV3FQDI235DUVLJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QEKJ57H4QITV3FQDI235DUVLJ6/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":"2026-06-21T23:38:09Z","links":{"resolver":"https://pith.science/pith/QEKJ57H4QITV3FQDI235DUVLJ6","bundle":"https://pith.science/pith/QEKJ57H4QITV3FQDI235DUVLJ6/bundle.json","state":"https://pith.science/pith/QEKJ57H4QITV3FQDI235DUVLJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QEKJ57H4QITV3FQDI235DUVLJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QEKJ57H4QITV3FQDI235DUVLJ6","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":"fce6470e9baf85ec495ca6ad04630422a91b4f18aca331f42668b76caa063747","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-15T16:55:30Z","title_canon_sha256":"c549c32c3c6ed7e2c3db3b76c08246f0e59d236090b9cdee16653ae15e7b725a"},"schema_version":"1.0","source":{"id":"1210.4102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4102","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4102v1","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4102","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"pith_short_12","alias_value":"QEKJ57H4QITV","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QEKJ57H4QITV3FQD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QEKJ57H4","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:166b40611e4e4c6621df6115cf1bc3b1757c7cf9e21fd0821e314a74f8396ebf","target":"graph","created_at":"2026-05-18T03:43:07Z","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":"This is a survey of recent results on manifolds with positive curvature from a series of lecture given in Guanajuato, Mexico in 2010. It also contains some hitsorical comments.","authors_text":"Wolfgang Ziller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-15T16:55:30Z","title":"Riemannian Manifolds with positive sectional curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4102","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:f559066b9ab8ce16f12b80c600c40407bad1825b1620712c0e8b12cc2f78045f","target":"record","created_at":"2026-05-18T03:43:07Z","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":"fce6470e9baf85ec495ca6ad04630422a91b4f18aca331f42668b76caa063747","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-15T16:55:30Z","title_canon_sha256":"c549c32c3c6ed7e2c3db3b76c08246f0e59d236090b9cdee16653ae15e7b725a"},"schema_version":"1.0","source":{"id":"1210.4102","kind":"arxiv","version":1}},"canonical_sha256":"81149efcfc82275d960346b7d1d2ab4fa4b20a89ef63a5a0ababe95517c09275","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81149efcfc82275d960346b7d1d2ab4fa4b20a89ef63a5a0ababe95517c09275","first_computed_at":"2026-05-18T03:43:07.996362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:07.996362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r6kIG4Gm0JRtm5wd/U9ol6OoA/V7nNJnkG6Ttqf7/v1OyPLO/CcZk/Zdp4gFKUvpFp3SX3jZSNuWmfVRnkQcAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:07.997084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f559066b9ab8ce16f12b80c600c40407bad1825b1620712c0e8b12cc2f78045f","sha256:166b40611e4e4c6621df6115cf1bc3b1757c7cf9e21fd0821e314a74f8396ebf"],"state_sha256":"0f48e5056f98613fe3632cd4c748cfc325dc844297c01ec3fbe4c6ec5a96ed46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nb7maUx8ErEBsocX8kr158pwHt23X53+hvyQVT6APYJJgIyjaRhNPxx0zoFxaiuwX+yfF8HKrNxp553Y4l4FAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:38:09.675357Z","bundle_sha256":"173c529c29478e60c1cf5d5094124f1ca26b096f8102b519d3588c6f0646991c"}}