{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OJHSXDYNSX3NWPYWVKZDTQCMJY","short_pith_number":"pith:OJHSXDYN","canonical_record":{"source":{"id":"1506.02018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-05T19:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"c7ce130bc5cef1ef03f3fe4d29822165f6fdfa8e4ab81e086ea1cada711ded99","abstract_canon_sha256":"9d4b8ef3cc164d5f0aac7e49ffd9fb3bd79f0eafadaae1d20b53560b264bee89"},"schema_version":"1.0"},"canonical_sha256":"724f2b8f0d95f6db3f16aab239c04c4e2a2b8c963796892224f2b48462ebc154","source":{"kind":"arxiv","id":"1506.02018","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02018","created_at":"2026-05-18T01:55:58Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02018v1","created_at":"2026-05-18T01:55:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02018","created_at":"2026-05-18T01:55:58Z"},{"alias_kind":"pith_short_12","alias_value":"OJHSXDYNSX3N","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OJHSXDYNSX3NWPYW","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OJHSXDYN","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OJHSXDYNSX3NWPYWVKZDTQCMJY","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-05T19:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"c7ce130bc5cef1ef03f3fe4d29822165f6fdfa8e4ab81e086ea1cada711ded99","abstract_canon_sha256":"9d4b8ef3cc164d5f0aac7e49ffd9fb3bd79f0eafadaae1d20b53560b264bee89"},"schema_version":"1.0"},"canonical_sha256":"724f2b8f0d95f6db3f16aab239c04c4e2a2b8c963796892224f2b48462ebc154","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:58.638981Z","signature_b64":"cCvRDJixlUzRUQzH9zMbX98ZUrXHFpmt4dva+LbPmX2CSUXhjt79DOPvLFKsV5TXC4Trfwj3AFrOlwPafa4kCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"724f2b8f0d95f6db3f16aab239c04c4e2a2b8c963796892224f2b48462ebc154","last_reissued_at":"2026-05-18T01:55:58.638496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:58.638496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02018","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":"2026-05-18T01:55:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oXHiQVWtz5IcxG21i2w0AehtPplnSukDUiNgro0d8DmTG0TYHjmNf6ISl5pZZAeCgXOZN1/V/cSH2J45zLwGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:30:17.359721Z"},"content_sha256":"fb960f033c8cbb2e16bf8ea33a6b7370299b15f7beca39665da47a91482c3382","schema_version":"1.0","event_id":"sha256:fb960f033c8cbb2e16bf8ea33a6b7370299b15f7beca39665da47a91482c3382"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OJHSXDYNSX3NWPYWVKZDTQCMJY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Blow up analysis for a cosmic strings equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriella Tarantello","submitted_at":"2015-06-05T19:23:46Z","abstract_excerpt":"In this paper we develop a blow up analysis for solutions of a planar semilinear elliptic equation involving exponential nonlinearities. Such solutions describe cosmic strings, and we show how their blow up behaviour is characterised by new and surprising phenomena. For example in some cases, the blow up profile of the solution is described in terms of a differential problem that bares a geometrical meaning in the context of the uniformization of the Riemann sphere with conical singularities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02018","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":"2026-05-18T01:55:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+D8gjbLzb9pmbmMPeBv7hmgHz/vFjhHEOEzredd74q3IJ3DsVIhLF/MrSsd9Nvi+/aofJXcWLc6s/uXd6GvGAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:30:17.360072Z"},"content_sha256":"ee8ca33825a746de6d3470b92b1ff3b34f5d15ef65102cf1bdd3d86cc135e3e0","schema_version":"1.0","event_id":"sha256:ee8ca33825a746de6d3470b92b1ff3b34f5d15ef65102cf1bdd3d86cc135e3e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJHSXDYNSX3NWPYWVKZDTQCMJY/bundle.json","state_url":"https://pith.science/pith/OJHSXDYNSX3NWPYWVKZDTQCMJY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJHSXDYNSX3NWPYWVKZDTQCMJY/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":"2026-06-23T06:30:17Z","links":{"resolver":"https://pith.science/pith/OJHSXDYNSX3NWPYWVKZDTQCMJY","bundle":"https://pith.science/pith/OJHSXDYNSX3NWPYWVKZDTQCMJY/bundle.json","state":"https://pith.science/pith/OJHSXDYNSX3NWPYWVKZDTQCMJY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJHSXDYNSX3NWPYWVKZDTQCMJY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OJHSXDYNSX3NWPYWVKZDTQCMJY","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":"9d4b8ef3cc164d5f0aac7e49ffd9fb3bd79f0eafadaae1d20b53560b264bee89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-05T19:23:46Z","title_canon_sha256":"c7ce130bc5cef1ef03f3fe4d29822165f6fdfa8e4ab81e086ea1cada711ded99"},"schema_version":"1.0","source":{"id":"1506.02018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02018","created_at":"2026-05-18T01:55:58Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02018v1","created_at":"2026-05-18T01:55:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02018","created_at":"2026-05-18T01:55:58Z"},{"alias_kind":"pith_short_12","alias_value":"OJHSXDYNSX3N","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OJHSXDYNSX3NWPYW","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OJHSXDYN","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:ee8ca33825a746de6d3470b92b1ff3b34f5d15ef65102cf1bdd3d86cc135e3e0","target":"graph","created_at":"2026-05-18T01:55:58Z","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 paper we develop a blow up analysis for solutions of a planar semilinear elliptic equation involving exponential nonlinearities. Such solutions describe cosmic strings, and we show how their blow up behaviour is characterised by new and surprising phenomena. For example in some cases, the blow up profile of the solution is described in terms of a differential problem that bares a geometrical meaning in the context of the uniformization of the Riemann sphere with conical singularities.","authors_text":"Gabriella Tarantello","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-05T19:23:46Z","title":"Blow up analysis for a cosmic strings equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02018","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:fb960f033c8cbb2e16bf8ea33a6b7370299b15f7beca39665da47a91482c3382","target":"record","created_at":"2026-05-18T01:55:58Z","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":"9d4b8ef3cc164d5f0aac7e49ffd9fb3bd79f0eafadaae1d20b53560b264bee89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-05T19:23:46Z","title_canon_sha256":"c7ce130bc5cef1ef03f3fe4d29822165f6fdfa8e4ab81e086ea1cada711ded99"},"schema_version":"1.0","source":{"id":"1506.02018","kind":"arxiv","version":1}},"canonical_sha256":"724f2b8f0d95f6db3f16aab239c04c4e2a2b8c963796892224f2b48462ebc154","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"724f2b8f0d95f6db3f16aab239c04c4e2a2b8c963796892224f2b48462ebc154","first_computed_at":"2026-05-18T01:55:58.638496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:58.638496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cCvRDJixlUzRUQzH9zMbX98ZUrXHFpmt4dva+LbPmX2CSUXhjt79DOPvLFKsV5TXC4Trfwj3AFrOlwPafa4kCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:58.638981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb960f033c8cbb2e16bf8ea33a6b7370299b15f7beca39665da47a91482c3382","sha256:ee8ca33825a746de6d3470b92b1ff3b34f5d15ef65102cf1bdd3d86cc135e3e0"],"state_sha256":"52feef13b9fb6e977d8ab0f8485f65bc37d3375e3fd791e3ebf2c6d9467ba82f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rSJSJpzfGYK+uSwbloBYeXrIKkwEFc8UgsI9wv7v1oF2hwprchc+EtkdR24/fUO7wlJT0FZ1POD6wGdtcmtCDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:30:17.362134Z","bundle_sha256":"fe331d2b9a79f105bfc0ceb78412fb37e0baf9f9e09138d80551cd72cbbe2767"}}