{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:D6XCYWPJR2CAHDXPLNWWCUYRYG","short_pith_number":"pith:D6XCYWPJ","canonical_record":{"source":{"id":"hep-th/9910104","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-10-14T03:48:35Z","cross_cats_sorted":[],"title_canon_sha256":"52f4bca32ce7e95a5d105c207a727dae5a2f990bf726c8449397ad2d1ff38791","abstract_canon_sha256":"3ac75b9c55fd7f0a216766af0b42b577a8e81bc89c2ae50e1346fe80798381a1"},"schema_version":"1.0"},"canonical_sha256":"1fae2c59e98e84038eef5b6d615311c19ff1685860ace33db70325c61d5fab4e","source":{"kind":"arxiv","id":"hep-th/9910104","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9910104","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9910104v1","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9910104","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"D6XCYWPJR2CA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"D6XCYWPJR2CAHDXP","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"D6XCYWPJ","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:D6XCYWPJR2CAHDXPLNWWCUYRYG","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9910104","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-10-14T03:48:35Z","cross_cats_sorted":[],"title_canon_sha256":"52f4bca32ce7e95a5d105c207a727dae5a2f990bf726c8449397ad2d1ff38791","abstract_canon_sha256":"3ac75b9c55fd7f0a216766af0b42b577a8e81bc89c2ae50e1346fe80798381a1"},"schema_version":"1.0"},"canonical_sha256":"1fae2c59e98e84038eef5b6d615311c19ff1685860ace33db70325c61d5fab4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:34.849230Z","signature_b64":"L6qRE8DcfZ2XTBu0xJ+G45WAYr1FpAiJSfBzq2sLrXwck4X2y0x9ZwPxy9JANyGzz6i6jdJnkPkeBhY3PQhMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fae2c59e98e84038eef5b6d615311c19ff1685860ace33db70325c61d5fab4e","last_reissued_at":"2026-05-18T01:38:34.848642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:34.848642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9910104","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":"2026-05-18T01:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T74ot2WukIJCRw6ZRiBRoysdx0b5rxGj75hA9loGayicc3w4MgzLU+x1GCC0EXpGypIixkdbigMFlCCCSB6zAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:30:55.749282Z"},"content_sha256":"6e5b586a19427b72c5aca1881b1d1b99a2784684db74b099af94bd70d4c4eed6","schema_version":"1.0","event_id":"sha256:6e5b586a19427b72c5aca1881b1d1b99a2784684db74b099af94bd70d4c4eed6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:D6XCYWPJR2CAHDXPLNWWCUYRYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The branch process of the cosmic strings","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Ying Jiang, Yishi Duan","submitted_at":"1999-10-14T03:48:35Z","abstract_excerpt":"In the light of $\\phi$-mapping method and the topological tensor current theory, the topological structure and the topological quantization of topological defects are obtained under the condition that Jacobian $J(\\phi/v)\\neq0$. When $J(\\phi/v)=0$, it is shown that there exists the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the generation, annihilation and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of $\\phi$-mapping, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9910104","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":"2026-05-18T01:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XqJEdjgxnOJPKlT5zNBRrDBqrvuC7qasPIDk8Xu6MSNp4ax6Fw0As2wl27p3rUeMnnklkxap1cGI8Vigwtq6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:30:55.749654Z"},"content_sha256":"527e04ed870fa8880db59dff13b8da097491a9b080bae7fccb1f4b471d4b2439","schema_version":"1.0","event_id":"sha256:527e04ed870fa8880db59dff13b8da097491a9b080bae7fccb1f4b471d4b2439"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6XCYWPJR2CAHDXPLNWWCUYRYG/bundle.json","state_url":"https://pith.science/pith/D6XCYWPJR2CAHDXPLNWWCUYRYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6XCYWPJR2CAHDXPLNWWCUYRYG/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":"2026-06-01T10:30:55Z","links":{"resolver":"https://pith.science/pith/D6XCYWPJR2CAHDXPLNWWCUYRYG","bundle":"https://pith.science/pith/D6XCYWPJR2CAHDXPLNWWCUYRYG/bundle.json","state":"https://pith.science/pith/D6XCYWPJR2CAHDXPLNWWCUYRYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6XCYWPJR2CAHDXPLNWWCUYRYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:D6XCYWPJR2CAHDXPLNWWCUYRYG","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":"3ac75b9c55fd7f0a216766af0b42b577a8e81bc89c2ae50e1346fe80798381a1","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-10-14T03:48:35Z","title_canon_sha256":"52f4bca32ce7e95a5d105c207a727dae5a2f990bf726c8449397ad2d1ff38791"},"schema_version":"1.0","source":{"id":"hep-th/9910104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9910104","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9910104v1","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9910104","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"D6XCYWPJR2CA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"D6XCYWPJR2CAHDXP","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"D6XCYWPJ","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:527e04ed870fa8880db59dff13b8da097491a9b080bae7fccb1f4b471d4b2439","target":"graph","created_at":"2026-05-18T01:38:34Z","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 the light of $\\phi$-mapping method and the topological tensor current theory, the topological structure and the topological quantization of topological defects are obtained under the condition that Jacobian $J(\\phi/v)\\neq0$. When $J(\\phi/v)=0$, it is shown that there exists the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the generation, annihilation and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of $\\phi$-mapping, respectively.","authors_text":"Ying Jiang, Yishi Duan","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1999-10-14T03:48:35Z","title":"The branch process of the cosmic strings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9910104","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":"sha256:6e5b586a19427b72c5aca1881b1d1b99a2784684db74b099af94bd70d4c4eed6","target":"record","created_at":"2026-05-18T01:38:34Z","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":"3ac75b9c55fd7f0a216766af0b42b577a8e81bc89c2ae50e1346fe80798381a1","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-10-14T03:48:35Z","title_canon_sha256":"52f4bca32ce7e95a5d105c207a727dae5a2f990bf726c8449397ad2d1ff38791"},"schema_version":"1.0","source":{"id":"hep-th/9910104","kind":"arxiv","version":1}},"canonical_sha256":"1fae2c59e98e84038eef5b6d615311c19ff1685860ace33db70325c61d5fab4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fae2c59e98e84038eef5b6d615311c19ff1685860ace33db70325c61d5fab4e","first_computed_at":"2026-05-18T01:38:34.848642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:34.848642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L6qRE8DcfZ2XTBu0xJ+G45WAYr1FpAiJSfBzq2sLrXwck4X2y0x9ZwPxy9JANyGzz6i6jdJnkPkeBhY3PQhMBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:34.849230Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9910104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e5b586a19427b72c5aca1881b1d1b99a2784684db74b099af94bd70d4c4eed6","sha256:527e04ed870fa8880db59dff13b8da097491a9b080bae7fccb1f4b471d4b2439"],"state_sha256":"c9bb6c58afe99ae9b9c8789b350969a6ea0cb97f8d92e807370f5fe7bf1a9b5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vHAOY3J/n86yABIbZ4TboqyuOBOAfeSs/6VZEGxbf89xM317jVjyJsXHJhFGJ3hzCFy0oCNgqUJp9Esv1rUdAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:30:55.751659Z","bundle_sha256":"6eb08a1aa1360a014758bbc3de030980137a60d44a08f3ea059021fb64267eff"}}