{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:ERST6BBNKCWTBYZMKVSFMAF3L3","short_pith_number":"pith:ERST6BBN","canonical_record":{"source":{"id":"0705.0491","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2007-05-03T15:57:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f1a7492a080780c61d8875cb8ea58cd2881915969571df3719bc39e17fa75692","abstract_canon_sha256":"5630c6f9615d7f899748e5207e3a6011a2ca910f8060a7c010bd41bd7cea2052"},"schema_version":"1.0"},"canonical_sha256":"24653f042d50ad30e32c55645600bb5edd958e1273c4bb017f07e3e148335321","source":{"kind":"arxiv","id":"0705.0491","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.0491","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"0705.0491v1","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.0491","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"ERST6BBNKCWT","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"ERST6BBNKCWTBYZM","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"ERST6BBN","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:ERST6BBNKCWTBYZMKVSFMAF3L3","target":"record","payload":{"canonical_record":{"source":{"id":"0705.0491","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2007-05-03T15:57:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f1a7492a080780c61d8875cb8ea58cd2881915969571df3719bc39e17fa75692","abstract_canon_sha256":"5630c6f9615d7f899748e5207e3a6011a2ca910f8060a7c010bd41bd7cea2052"},"schema_version":"1.0"},"canonical_sha256":"24653f042d50ad30e32c55645600bb5edd958e1273c4bb017f07e3e148335321","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:28.545472Z","signature_b64":"7Jr/iaFmPSwgwLn1wn/OaQEnlT9Zcpqlt1ebWhjXNmPDB26ulABcDM0qiTU1j2uwCp1kPg7CB5BjqCdSOFQ0DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24653f042d50ad30e32c55645600bb5edd958e1273c4bb017f07e3e148335321","last_reissued_at":"2026-05-18T01:18:28.544958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:28.544958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0705.0491","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":"2026-05-18T01:18:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w2csjASP18dZhrTS3sYHjh9SEwPaUPETxsfEGVph4MzKrlA0gbX3K9igKPdqwrMv0dhoET4a0uHeIfAAREXyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:11:27.720474Z"},"content_sha256":"fe88fa76d611aa70f6d8774ac27e4b2472e7e42ec5e6afebd448089045406ae7","schema_version":"1.0","event_id":"sha256:fe88fa76d611aa70f6d8774ac27e4b2472e7e42ec5e6afebd448089045406ae7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:ERST6BBNKCWTBYZMKVSFMAF3L3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the blow-up threshold for weakly coupled nonlinear Schroedinger equations","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Eugenio Montefusco, Luca Fanelli","submitted_at":"2007-05-03T15:57:45Z","abstract_excerpt":"We study the Cauchy problem for a system of two coupled nonlinear focusing Schroedinger equations arising in nonlinear optics. We discuss when the solutions are global in time or blow-up in finite time. Some results, in dependence of the data of the problem, are proved; in particular we give a bound, depending on the coupling parameter, for the blow-up threshold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.0491","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":"2026-05-18T01:18:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/yrrUip0D6ksO3GNLsSQsDQ+U2Afo/m0On88FZ3AKcyXPpAd7+f/5HPlzv2Hnbdb1/t+ze4RoJaHXp02uSVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:11:27.720824Z"},"content_sha256":"0d2fb56c8f300f9c67a505181866087e55c8ac7312ad638a0974728d751e6057","schema_version":"1.0","event_id":"sha256:0d2fb56c8f300f9c67a505181866087e55c8ac7312ad638a0974728d751e6057"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERST6BBNKCWTBYZMKVSFMAF3L3/bundle.json","state_url":"https://pith.science/pith/ERST6BBNKCWTBYZMKVSFMAF3L3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERST6BBNKCWTBYZMKVSFMAF3L3/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":"2026-06-05T12:11:27Z","links":{"resolver":"https://pith.science/pith/ERST6BBNKCWTBYZMKVSFMAF3L3","bundle":"https://pith.science/pith/ERST6BBNKCWTBYZMKVSFMAF3L3/bundle.json","state":"https://pith.science/pith/ERST6BBNKCWTBYZMKVSFMAF3L3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERST6BBNKCWTBYZMKVSFMAF3L3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ERST6BBNKCWTBYZMKVSFMAF3L3","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":"5630c6f9615d7f899748e5207e3a6011a2ca910f8060a7c010bd41bd7cea2052","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.AP","submitted_at":"2007-05-03T15:57:45Z","title_canon_sha256":"f1a7492a080780c61d8875cb8ea58cd2881915969571df3719bc39e17fa75692"},"schema_version":"1.0","source":{"id":"0705.0491","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.0491","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"0705.0491v1","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.0491","created_at":"2026-05-18T01:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"ERST6BBNKCWT","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"ERST6BBNKCWTBYZM","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"ERST6BBN","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:0d2fb56c8f300f9c67a505181866087e55c8ac7312ad638a0974728d751e6057","target":"graph","created_at":"2026-05-18T01:18:28Z","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 study the Cauchy problem for a system of two coupled nonlinear focusing Schroedinger equations arising in nonlinear optics. We discuss when the solutions are global in time or blow-up in finite time. Some results, in dependence of the data of the problem, are proved; in particular we give a bound, depending on the coupling parameter, for the blow-up threshold.","authors_text":"Eugenio Montefusco, Luca Fanelli","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2007-05-03T15:57:45Z","title":"On the blow-up threshold for weakly coupled nonlinear Schroedinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.0491","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:fe88fa76d611aa70f6d8774ac27e4b2472e7e42ec5e6afebd448089045406ae7","target":"record","created_at":"2026-05-18T01:18:28Z","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":"5630c6f9615d7f899748e5207e3a6011a2ca910f8060a7c010bd41bd7cea2052","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.AP","submitted_at":"2007-05-03T15:57:45Z","title_canon_sha256":"f1a7492a080780c61d8875cb8ea58cd2881915969571df3719bc39e17fa75692"},"schema_version":"1.0","source":{"id":"0705.0491","kind":"arxiv","version":1}},"canonical_sha256":"24653f042d50ad30e32c55645600bb5edd958e1273c4bb017f07e3e148335321","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24653f042d50ad30e32c55645600bb5edd958e1273c4bb017f07e3e148335321","first_computed_at":"2026-05-18T01:18:28.544958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:28.544958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Jr/iaFmPSwgwLn1wn/OaQEnlT9Zcpqlt1ebWhjXNmPDB26ulABcDM0qiTU1j2uwCp1kPg7CB5BjqCdSOFQ0DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:28.545472Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.0491","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe88fa76d611aa70f6d8774ac27e4b2472e7e42ec5e6afebd448089045406ae7","sha256:0d2fb56c8f300f9c67a505181866087e55c8ac7312ad638a0974728d751e6057"],"state_sha256":"e5fb1106c33cb53f26239d4753e8767550fe4ee13ad3e9076c85326f4a816832"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bE5OjrFA1Ih+hOqgWZ0ZKyiv9ko/8cqQrOfVHICWHBOr/gQFS+DYtcAaQjlTAA8I7fUk0jQBw220N/xj4R1uDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:11:27.722748Z","bundle_sha256":"6b2ab2f774e6aed42be647b74e099758cfee6f6127e1c21c4f3bd08b53ce9e3d"}}