{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7FLDAIIZFTHYUG34YOLJAL5IOQ","short_pith_number":"pith:7FLDAIIZ","canonical_record":{"source":{"id":"2403.10959","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-03-16T16:16:08Z","cross_cats_sorted":[],"title_canon_sha256":"95eb0f4bca7da3a51cf029ef5da430f1dfe201135097159a76781bbbfd3fb30d","abstract_canon_sha256":"920d640c2cf04e137d5bab6226680756ee354f5bed709055e6e6fab0ca034db3"},"schema_version":"1.0"},"canonical_sha256":"f9563021192ccf8a1b7cc396902fa87420db96d56ae5c05698707a42df9759c8","source":{"kind":"arxiv","id":"2403.10959","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.10959","created_at":"2026-07-05T09:49:03Z"},{"alias_kind":"arxiv_version","alias_value":"2403.10959v2","created_at":"2026-07-05T09:49:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.10959","created_at":"2026-07-05T09:49:03Z"},{"alias_kind":"pith_short_12","alias_value":"7FLDAIIZFTHY","created_at":"2026-07-05T09:49:03Z"},{"alias_kind":"pith_short_16","alias_value":"7FLDAIIZFTHYUG34","created_at":"2026-07-05T09:49:03Z"},{"alias_kind":"pith_short_8","alias_value":"7FLDAIIZ","created_at":"2026-07-05T09:49:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7FLDAIIZFTHYUG34YOLJAL5IOQ","target":"record","payload":{"canonical_record":{"source":{"id":"2403.10959","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-03-16T16:16:08Z","cross_cats_sorted":[],"title_canon_sha256":"95eb0f4bca7da3a51cf029ef5da430f1dfe201135097159a76781bbbfd3fb30d","abstract_canon_sha256":"920d640c2cf04e137d5bab6226680756ee354f5bed709055e6e6fab0ca034db3"},"schema_version":"1.0"},"canonical_sha256":"f9563021192ccf8a1b7cc396902fa87420db96d56ae5c05698707a42df9759c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:49:03.495301Z","signature_b64":"N8rYwy2QitPy+7LqJKWARRrLEcREf+sYo0tGs5FTZgbcSSTaljkKliF6SyFXQP+EpNbqeuhPP5ha+sI59F/SBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9563021192ccf8a1b7cc396902fa87420db96d56ae5c05698707a42df9759c8","last_reissued_at":"2026-07-05T09:49:03.494654Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:49:03.494654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.10959","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":"2026-07-05T09:49:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+a6TOl4oxm8mOC+xmDyFCHJOzS/rVztDx2hSaG6ZtDcevLDFtbjCwkju6o1D3+pZDk3h1SwJ+KtS2hn7O+ECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T06:55:00.074201Z"},"content_sha256":"4b660e3f7041e60d93d3449c10650d91e822e24880e7c297e46d81df54c4d2a3","schema_version":"1.0","event_id":"sha256:4b660e3f7041e60d93d3449c10650d91e822e24880e7c297e46d81df54c4d2a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7FLDAIIZFTHYUG34YOLJAL5IOQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinitely many normalized solutions of $L^2$-supercritical NLS equations on noncompact metric graphs with localized nonlinearities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christophe Troestler, Damien Galant, Louis Jeanjean, Pablo Carrillo","submitted_at":"2024-03-16T16:16:08Z","abstract_excerpt":"We consider the existence of solutions for nonlinear Schr\\\"odinger equations on noncompact metric graphs with localized nonlinearities. In an $L^2$-supercritical regime, we establish the existence of infinitely many solutions for any prescribed mass."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.10959","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.10959/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:49:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SLpRsrZcnCZDUahELuMonuALKeRsh/0Fu+NNjLAM36t9dCZDh0FZ0ZFzpUuW5rjq1z57VR3OxOFkiFtgyADlDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T06:55:00.074700Z"},"content_sha256":"40a3504a967203e9c0f044cf5e416ee9bc6aafbe3cb73bd0a3903bf65acdbe52","schema_version":"1.0","event_id":"sha256:40a3504a967203e9c0f044cf5e416ee9bc6aafbe3cb73bd0a3903bf65acdbe52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FLDAIIZFTHYUG34YOLJAL5IOQ/bundle.json","state_url":"https://pith.science/pith/7FLDAIIZFTHYUG34YOLJAL5IOQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FLDAIIZFTHYUG34YOLJAL5IOQ/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":"2026-08-15T06:55:00Z","links":{"resolver":"https://pith.science/pith/7FLDAIIZFTHYUG34YOLJAL5IOQ","bundle":"https://pith.science/pith/7FLDAIIZFTHYUG34YOLJAL5IOQ/bundle.json","state":"https://pith.science/pith/7FLDAIIZFTHYUG34YOLJAL5IOQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FLDAIIZFTHYUG34YOLJAL5IOQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7FLDAIIZFTHYUG34YOLJAL5IOQ","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":"920d640c2cf04e137d5bab6226680756ee354f5bed709055e6e6fab0ca034db3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-03-16T16:16:08Z","title_canon_sha256":"95eb0f4bca7da3a51cf029ef5da430f1dfe201135097159a76781bbbfd3fb30d"},"schema_version":"1.0","source":{"id":"2403.10959","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.10959","created_at":"2026-07-05T09:49:03Z"},{"alias_kind":"arxiv_version","alias_value":"2403.10959v2","created_at":"2026-07-05T09:49:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.10959","created_at":"2026-07-05T09:49:03Z"},{"alias_kind":"pith_short_12","alias_value":"7FLDAIIZFTHY","created_at":"2026-07-05T09:49:03Z"},{"alias_kind":"pith_short_16","alias_value":"7FLDAIIZFTHYUG34","created_at":"2026-07-05T09:49:03Z"},{"alias_kind":"pith_short_8","alias_value":"7FLDAIIZ","created_at":"2026-07-05T09:49:03Z"}],"graph_snapshots":[{"event_id":"sha256:40a3504a967203e9c0f044cf5e416ee9bc6aafbe3cb73bd0a3903bf65acdbe52","target":"graph","created_at":"2026-07-05T09:49:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.10959/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the existence of solutions for nonlinear Schr\\\"odinger equations on noncompact metric graphs with localized nonlinearities. In an $L^2$-supercritical regime, we establish the existence of infinitely many solutions for any prescribed mass.","authors_text":"Christophe Troestler, Damien Galant, Louis Jeanjean, Pablo Carrillo","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-03-16T16:16:08Z","title":"Infinitely many normalized solutions of $L^2$-supercritical NLS equations on noncompact metric graphs with localized nonlinearities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.10959","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":"sha256:4b660e3f7041e60d93d3449c10650d91e822e24880e7c297e46d81df54c4d2a3","target":"record","created_at":"2026-07-05T09:49:03Z","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":"920d640c2cf04e137d5bab6226680756ee354f5bed709055e6e6fab0ca034db3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-03-16T16:16:08Z","title_canon_sha256":"95eb0f4bca7da3a51cf029ef5da430f1dfe201135097159a76781bbbfd3fb30d"},"schema_version":"1.0","source":{"id":"2403.10959","kind":"arxiv","version":2}},"canonical_sha256":"f9563021192ccf8a1b7cc396902fa87420db96d56ae5c05698707a42df9759c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9563021192ccf8a1b7cc396902fa87420db96d56ae5c05698707a42df9759c8","first_computed_at":"2026-07-05T09:49:03.494654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:49:03.494654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N8rYwy2QitPy+7LqJKWARRrLEcREf+sYo0tGs5FTZgbcSSTaljkKliF6SyFXQP+EpNbqeuhPP5ha+sI59F/SBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:49:03.495301Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.10959","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b660e3f7041e60d93d3449c10650d91e822e24880e7c297e46d81df54c4d2a3","sha256:40a3504a967203e9c0f044cf5e416ee9bc6aafbe3cb73bd0a3903bf65acdbe52"],"state_sha256":"645b71a72e299f6a1512cc5d83aad7e53e64ee6c8c695e0cc9c5cee5a729fe45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bGCSQXx43GliK5essgxPgfT4Gztb2wEtlk3P0CrWmtrV7snSbvJeArYA2NgeHPNf9azTcXY6m2UV0SYwY8zcBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T06:55:00.080162Z","bundle_sha256":"fb24ec41304d89318d1fc6cc2113c0f786c4ca26acac447b7220bfc3afa31edc"}}