{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5ZEGYKILLRUE2OQLOWTO3FRCZY","short_pith_number":"pith:5ZEGYKIL","canonical_record":{"source":{"id":"1007.0077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-07-01T06:45:36Z","cross_cats_sorted":[],"title_canon_sha256":"731b408a1da7ec5d6176360f40b2e789599511cba47dd7e18fdf5545f2be5d76","abstract_canon_sha256":"3206d2222b0b9e402f344b1ee7bff201026dec39125a5dcc3102ac62ff1d7b82"},"schema_version":"1.0"},"canonical_sha256":"ee486c290b5c684d3a0b75a6ed9622ce39a7ee64010890e61de2cb444982ed13","source":{"kind":"arxiv","id":"1007.0077","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0077","created_at":"2026-05-18T04:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0077v2","created_at":"2026-05-18T04:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0077","created_at":"2026-05-18T04:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"5ZEGYKILLRUE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5ZEGYKILLRUE2OQL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5ZEGYKIL","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5ZEGYKILLRUE2OQLOWTO3FRCZY","target":"record","payload":{"canonical_record":{"source":{"id":"1007.0077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-07-01T06:45:36Z","cross_cats_sorted":[],"title_canon_sha256":"731b408a1da7ec5d6176360f40b2e789599511cba47dd7e18fdf5545f2be5d76","abstract_canon_sha256":"3206d2222b0b9e402f344b1ee7bff201026dec39125a5dcc3102ac62ff1d7b82"},"schema_version":"1.0"},"canonical_sha256":"ee486c290b5c684d3a0b75a6ed9622ce39a7ee64010890e61de2cb444982ed13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:55.831048Z","signature_b64":"GJmpj8FYMcGzEyWrxQYBqwz6BMaZULbXVLJm7xhG2y/velaDWnETAUXMwNelCeWwaH2J1dayakUE2I0yEor1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee486c290b5c684d3a0b75a6ed9622ce39a7ee64010890e61de2cb444982ed13","last_reissued_at":"2026-05-18T04:40:55.830351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:55.830351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.0077","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ikrC2xYMw4pwt1D67fg1U2P9UzyPh9I/EjwM7S7vmqX7h/PKpYIKfisOyVhwmRDCwi7zu4xj2frv4IvGzfmLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:46:45.378041Z"},"content_sha256":"486d2081bc297ee4abc20f39263267098e56965671259098df5dccc16bf80d34","schema_version":"1.0","event_id":"sha256:486d2081bc297ee4abc20f39263267098e56965671259098df5dccc16bf80d34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5ZEGYKILLRUE2OQLOWTO3FRCZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite time extinction by nonlinear damping for Schrodinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cl\\'ement Gallo (I3M), R\\'emi Carles (I3M)","submitted_at":"2010-07-01T06:45:36Z","abstract_excerpt":"We consider the Schrodinger equation on a compact manifold, in the presence of a nonlinear damping term, which is homogeneous and sublinear. For initial data in the energy space, we construct a weak solution, defined for all positive time, which is shown to be unique. In the one-dimensional case, we show that it becomes zero in finite time. In the two and three-dimensional cases, we prove the same result under the assumption of extra regularity on the initial datum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0077","kind":"arxiv","version":2},"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":"2026-05-18T04:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NpcGsfwOs9pJ485/QLh87ErE91rdBAuGnMSJJKtV+tgJLe0lpSId6kl+0t91QbIQdObtMO2fANl/+EjN41e0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:46:45.378392Z"},"content_sha256":"bf2f3ca0ad41985346ac65042f3a3e4bbfc2eede012afb2e1182ddd695e86410","schema_version":"1.0","event_id":"sha256:bf2f3ca0ad41985346ac65042f3a3e4bbfc2eede012afb2e1182ddd695e86410"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ZEGYKILLRUE2OQLOWTO3FRCZY/bundle.json","state_url":"https://pith.science/pith/5ZEGYKILLRUE2OQLOWTO3FRCZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ZEGYKILLRUE2OQLOWTO3FRCZY/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":"2026-07-06T20:46:45Z","links":{"resolver":"https://pith.science/pith/5ZEGYKILLRUE2OQLOWTO3FRCZY","bundle":"https://pith.science/pith/5ZEGYKILLRUE2OQLOWTO3FRCZY/bundle.json","state":"https://pith.science/pith/5ZEGYKILLRUE2OQLOWTO3FRCZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ZEGYKILLRUE2OQLOWTO3FRCZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5ZEGYKILLRUE2OQLOWTO3FRCZY","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":"3206d2222b0b9e402f344b1ee7bff201026dec39125a5dcc3102ac62ff1d7b82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-07-01T06:45:36Z","title_canon_sha256":"731b408a1da7ec5d6176360f40b2e789599511cba47dd7e18fdf5545f2be5d76"},"schema_version":"1.0","source":{"id":"1007.0077","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0077","created_at":"2026-05-18T04:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0077v2","created_at":"2026-05-18T04:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0077","created_at":"2026-05-18T04:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"5ZEGYKILLRUE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5ZEGYKILLRUE2OQL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5ZEGYKIL","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:bf2f3ca0ad41985346ac65042f3a3e4bbfc2eede012afb2e1182ddd695e86410","target":"graph","created_at":"2026-05-18T04:40:55Z","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 consider the Schrodinger equation on a compact manifold, in the presence of a nonlinear damping term, which is homogeneous and sublinear. For initial data in the energy space, we construct a weak solution, defined for all positive time, which is shown to be unique. In the one-dimensional case, we show that it becomes zero in finite time. In the two and three-dimensional cases, we prove the same result under the assumption of extra regularity on the initial datum.","authors_text":"Cl\\'ement Gallo (I3M), R\\'emi Carles (I3M)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-07-01T06:45:36Z","title":"Finite time extinction by nonlinear damping for Schrodinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0077","kind":"arxiv","version":2},"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":"sha256:486d2081bc297ee4abc20f39263267098e56965671259098df5dccc16bf80d34","target":"record","created_at":"2026-05-18T04:40:55Z","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":"3206d2222b0b9e402f344b1ee7bff201026dec39125a5dcc3102ac62ff1d7b82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-07-01T06:45:36Z","title_canon_sha256":"731b408a1da7ec5d6176360f40b2e789599511cba47dd7e18fdf5545f2be5d76"},"schema_version":"1.0","source":{"id":"1007.0077","kind":"arxiv","version":2}},"canonical_sha256":"ee486c290b5c684d3a0b75a6ed9622ce39a7ee64010890e61de2cb444982ed13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee486c290b5c684d3a0b75a6ed9622ce39a7ee64010890e61de2cb444982ed13","first_computed_at":"2026-05-18T04:40:55.830351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:55.830351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GJmpj8FYMcGzEyWrxQYBqwz6BMaZULbXVLJm7xhG2y/velaDWnETAUXMwNelCeWwaH2J1dayakUE2I0yEor1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:55.831048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0077","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:486d2081bc297ee4abc20f39263267098e56965671259098df5dccc16bf80d34","sha256:bf2f3ca0ad41985346ac65042f3a3e4bbfc2eede012afb2e1182ddd695e86410"],"state_sha256":"04e47671e43152e80cdc5e85c677b35692dfa8282341037a0f1bd9fa1dd2f4ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6QsmoJ6xgYJYQ2lNN8ai1WHiygoqn03ZK5y5JmzBnbWYJQE9LNv32fj9SUm7KOGXNaUQWNPVC9ZJWCjKgutqBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T20:46:45.380173Z","bundle_sha256":"6cc8039027197aed8a7e5c740e1a9ee4ab50ad9c1be3744e1ac31d8b4015c441"}}