{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6T4GK6KMRG6MOHV4B6HQOGWNY3","short_pith_number":"pith:6T4GK6KM","canonical_record":{"source":{"id":"1505.01994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-08T11:08:35Z","cross_cats_sorted":[],"title_canon_sha256":"4e4f0db6445fc6694b1afe8604121e4c173a4f0b8b33f6244634a7c6ad16412c","abstract_canon_sha256":"2222700e53ac94fd81353ccac9ec7c1a9816fa5b9f8d3eeb23e856ad860c8eeb"},"schema_version":"1.0"},"canonical_sha256":"f4f865794c89bcc71ebc0f8f071acdc6c011f74c59545b4a6c39669475735775","source":{"kind":"arxiv","id":"1505.01994","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01994","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01994v1","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01994","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"pith_short_12","alias_value":"6T4GK6KMRG6M","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6T4GK6KMRG6MOHV4","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6T4GK6KM","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6T4GK6KMRG6MOHV4B6HQOGWNY3","target":"record","payload":{"canonical_record":{"source":{"id":"1505.01994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-08T11:08:35Z","cross_cats_sorted":[],"title_canon_sha256":"4e4f0db6445fc6694b1afe8604121e4c173a4f0b8b33f6244634a7c6ad16412c","abstract_canon_sha256":"2222700e53ac94fd81353ccac9ec7c1a9816fa5b9f8d3eeb23e856ad860c8eeb"},"schema_version":"1.0"},"canonical_sha256":"f4f865794c89bcc71ebc0f8f071acdc6c011f74c59545b4a6c39669475735775","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:40.737763Z","signature_b64":"/hoK/EfAffIfzhyEFbRC5Ft6l5P3lkn+JVd7xm0oaDzP8BLNi3Dt5p15HX24qvhWKgDLU5m++puDtfhqHS6dAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4f865794c89bcc71ebc0f8f071acdc6c011f74c59545b4a6c39669475735775","last_reissued_at":"2026-05-18T01:21:40.737277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:40.737277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.01994","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":"2026-05-18T01:21:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P4CBmRYd6CMeJXe0Hrui9dqS/QtkYnWuHNJNV6h76M2emt1/R6nbaQmmPsCbxkEFdqCwB7hjJJkMmeTrMFutBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:24:44.904501Z"},"content_sha256":"59d3ebaec7b34c0a9cc49b7b804de527e6e0fe93e49880b43534ff601ba661f6","schema_version":"1.0","event_id":"sha256:59d3ebaec7b34c0a9cc49b7b804de527e6e0fe93e49880b43534ff601ba661f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6T4GK6KMRG6MOHV4B6HQOGWNY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical metrics with conical singularities on a 2-sphere: angle constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dmitri Panov, Gabriele Mondello","submitted_at":"2015-05-08T11:08:35Z","abstract_excerpt":"In this article we give a criterion for the existence of a metric of curvature $1$ on a $2$-sphere with $n$ conical singularities of prescribed angles $2\\pi\\vartheta_1,\\dots,2\\pi\\vartheta_n$ and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in $\\vartheta_1,\\dots,\\vartheta_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01994","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":"2026-05-18T01:21:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pL/v1+s6ystINX59w7vaV9OY/VTsXUezveX24Bj6sWO1gaj6xTRdp7F1/Dp7ydzq+QmUMmz6Di5xGsWZGVFEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:24:44.904923Z"},"content_sha256":"9879811df9221bccf4e2255e6253d42ab4a9f0bf25b9a66610378ca91aa0c9fb","schema_version":"1.0","event_id":"sha256:9879811df9221bccf4e2255e6253d42ab4a9f0bf25b9a66610378ca91aa0c9fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6T4GK6KMRG6MOHV4B6HQOGWNY3/bundle.json","state_url":"https://pith.science/pith/6T4GK6KMRG6MOHV4B6HQOGWNY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6T4GK6KMRG6MOHV4B6HQOGWNY3/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":"2026-06-24T08:24:44Z","links":{"resolver":"https://pith.science/pith/6T4GK6KMRG6MOHV4B6HQOGWNY3","bundle":"https://pith.science/pith/6T4GK6KMRG6MOHV4B6HQOGWNY3/bundle.json","state":"https://pith.science/pith/6T4GK6KMRG6MOHV4B6HQOGWNY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6T4GK6KMRG6MOHV4B6HQOGWNY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6T4GK6KMRG6MOHV4B6HQOGWNY3","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":"2222700e53ac94fd81353ccac9ec7c1a9816fa5b9f8d3eeb23e856ad860c8eeb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-08T11:08:35Z","title_canon_sha256":"4e4f0db6445fc6694b1afe8604121e4c173a4f0b8b33f6244634a7c6ad16412c"},"schema_version":"1.0","source":{"id":"1505.01994","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01994","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01994v1","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01994","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"pith_short_12","alias_value":"6T4GK6KMRG6M","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6T4GK6KMRG6MOHV4","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6T4GK6KM","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:9879811df9221bccf4e2255e6253d42ab4a9f0bf25b9a66610378ca91aa0c9fb","target":"graph","created_at":"2026-05-18T01:21:40Z","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":"In this article we give a criterion for the existence of a metric of curvature $1$ on a $2$-sphere with $n$ conical singularities of prescribed angles $2\\pi\\vartheta_1,\\dots,2\\pi\\vartheta_n$ and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in $\\vartheta_1,\\dots,\\vartheta_n$.","authors_text":"Dmitri Panov, Gabriele Mondello","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-08T11:08:35Z","title":"Spherical metrics with conical singularities on a 2-sphere: angle constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01994","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":"sha256:59d3ebaec7b34c0a9cc49b7b804de527e6e0fe93e49880b43534ff601ba661f6","target":"record","created_at":"2026-05-18T01:21:40Z","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":"2222700e53ac94fd81353ccac9ec7c1a9816fa5b9f8d3eeb23e856ad860c8eeb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-08T11:08:35Z","title_canon_sha256":"4e4f0db6445fc6694b1afe8604121e4c173a4f0b8b33f6244634a7c6ad16412c"},"schema_version":"1.0","source":{"id":"1505.01994","kind":"arxiv","version":1}},"canonical_sha256":"f4f865794c89bcc71ebc0f8f071acdc6c011f74c59545b4a6c39669475735775","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4f865794c89bcc71ebc0f8f071acdc6c011f74c59545b4a6c39669475735775","first_computed_at":"2026-05-18T01:21:40.737277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:40.737277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/hoK/EfAffIfzhyEFbRC5Ft6l5P3lkn+JVd7xm0oaDzP8BLNi3Dt5p15HX24qvhWKgDLU5m++puDtfhqHS6dAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:40.737763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.01994","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59d3ebaec7b34c0a9cc49b7b804de527e6e0fe93e49880b43534ff601ba661f6","sha256:9879811df9221bccf4e2255e6253d42ab4a9f0bf25b9a66610378ca91aa0c9fb"],"state_sha256":"f7a9272fde04abaee1d7a635107d3b2a10da4598031779b2fafa47a4c0e3acb0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NYfbzm2Vzu1ddX32LB7aUPc/iRoOWobceUrKJYMFaMVfeV4mdssiMeybrom6knmcAuou7nSTaFunP2MM1EAJDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:24:44.907106Z","bundle_sha256":"a20a8d5af5f428f6034e1c6fc65306cb8ffb7a207ec4d72a21faf16796860e0e"}}