{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HXOX7HOA72T2BBPGOUNEWOTEKW","short_pith_number":"pith:HXOX7HOA","canonical_record":{"source":{"id":"2501.05389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-09T17:22:38Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"13835dd61631cb0143d7c6cbbc2dbbdec37de4edb0ee743a696460000a6f6b84","abstract_canon_sha256":"99a354231f31aab66ec88706885a7e0b3f55674742ac937bf0329a6529668e1a"},"schema_version":"1.0"},"canonical_sha256":"3ddd7f9dc0fea7a085e6751a4b3a6455b232a7a0f3fe7cd6351e5d23621d6976","source":{"kind":"arxiv","id":"2501.05389","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.05389","created_at":"2026-07-05T10:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"2501.05389v2","created_at":"2026-07-05T10:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.05389","created_at":"2026-07-05T10:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"HXOX7HOA72T2","created_at":"2026-07-05T10:41:51Z"},{"alias_kind":"pith_short_16","alias_value":"HXOX7HOA72T2BBPG","created_at":"2026-07-05T10:41:51Z"},{"alias_kind":"pith_short_8","alias_value":"HXOX7HOA","created_at":"2026-07-05T10:41:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HXOX7HOA72T2BBPGOUNEWOTEKW","target":"record","payload":{"canonical_record":{"source":{"id":"2501.05389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-09T17:22:38Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"13835dd61631cb0143d7c6cbbc2dbbdec37de4edb0ee743a696460000a6f6b84","abstract_canon_sha256":"99a354231f31aab66ec88706885a7e0b3f55674742ac937bf0329a6529668e1a"},"schema_version":"1.0"},"canonical_sha256":"3ddd7f9dc0fea7a085e6751a4b3a6455b232a7a0f3fe7cd6351e5d23621d6976","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:41:51.745861Z","signature_b64":"W+deERlPZkeE9mRum3sRPXrniP7p6kZ8F9Tk+H5A6GiSiDh6HURQPFSb8cAbLX2rrQYb8K/G2C0N1s+nJO4gBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ddd7f9dc0fea7a085e6751a4b3a6455b232a7a0f3fe7cd6351e5d23621d6976","last_reissued_at":"2026-07-05T10:41:51.745435Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:41:51.745435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.05389","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":"2026-07-05T10:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ewe1EqiowmMmQxTxauasLYmJaqE6y0sHOm7QJ/5fzcn4zZGSZijrk0x8ECZV1b99dKyoTQQGDc8uc1zHcw/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:59:53.864586Z"},"content_sha256":"95326e9e1f0a6921a2e06cc3049bebbfc7a9fbb37c731c10f9774010a680852c","schema_version":"1.0","event_id":"sha256:95326e9e1f0a6921a2e06cc3049bebbfc7a9fbb37c731c10f9774010a680852c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HXOX7HOA72T2BBPGOUNEWOTEKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dafermos' principle and Brenier's duality scheme for defocusing dispersive equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Dmitry Vorotnikov","submitted_at":"2025-01-09T17:22:38Z","abstract_excerpt":"We discover an abstract structure behind several nonlinear dispersive equations (including the NLS, NLKG and GKdV equations with generic defocusing power-law nonlinearities) that is reminiscent of hyperbolic conservation laws. The underlying abstract problem admits an \"entropy\" that is formally conserved. The entropy is determined by a strictly convex function that naturally generates an anisotropic Orlicz space. For such problems, we introduce the dual matrix-valued variational formulation in the spirit of [Y. Brenier. Comm. Math. Phys. (2018) 364(2) 579-605]. Employing time-adaptive weights,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05389","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/2501.05389/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":"2026-07-05T10:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6h0tjtKKboNxus7qyh1l5LCGuwWEmpjupL9PtfPtXy4AHvpFXH9ecx8NaoSeGSbveu5bkLTKby9EklMS24c1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:59:53.864911Z"},"content_sha256":"d70cef9955d3ceebdaef86e0df86ff340cc1f5d009bc74b004f866bd8dfac86f","schema_version":"1.0","event_id":"sha256:d70cef9955d3ceebdaef86e0df86ff340cc1f5d009bc74b004f866bd8dfac86f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HXOX7HOA72T2BBPGOUNEWOTEKW/bundle.json","state_url":"https://pith.science/pith/HXOX7HOA72T2BBPGOUNEWOTEKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HXOX7HOA72T2BBPGOUNEWOTEKW/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":"2026-08-14T06:59:53Z","links":{"resolver":"https://pith.science/pith/HXOX7HOA72T2BBPGOUNEWOTEKW","bundle":"https://pith.science/pith/HXOX7HOA72T2BBPGOUNEWOTEKW/bundle.json","state":"https://pith.science/pith/HXOX7HOA72T2BBPGOUNEWOTEKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HXOX7HOA72T2BBPGOUNEWOTEKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HXOX7HOA72T2BBPGOUNEWOTEKW","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":"99a354231f31aab66ec88706885a7e0b3f55674742ac937bf0329a6529668e1a","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-09T17:22:38Z","title_canon_sha256":"13835dd61631cb0143d7c6cbbc2dbbdec37de4edb0ee743a696460000a6f6b84"},"schema_version":"1.0","source":{"id":"2501.05389","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.05389","created_at":"2026-07-05T10:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"2501.05389v2","created_at":"2026-07-05T10:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.05389","created_at":"2026-07-05T10:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"HXOX7HOA72T2","created_at":"2026-07-05T10:41:51Z"},{"alias_kind":"pith_short_16","alias_value":"HXOX7HOA72T2BBPG","created_at":"2026-07-05T10:41:51Z"},{"alias_kind":"pith_short_8","alias_value":"HXOX7HOA","created_at":"2026-07-05T10:41:51Z"}],"graph_snapshots":[{"event_id":"sha256:d70cef9955d3ceebdaef86e0df86ff340cc1f5d009bc74b004f866bd8dfac86f","target":"graph","created_at":"2026-07-05T10:41:51Z","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/2501.05389/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discover an abstract structure behind several nonlinear dispersive equations (including the NLS, NLKG and GKdV equations with generic defocusing power-law nonlinearities) that is reminiscent of hyperbolic conservation laws. The underlying abstract problem admits an \"entropy\" that is formally conserved. The entropy is determined by a strictly convex function that naturally generates an anisotropic Orlicz space. For such problems, we introduce the dual matrix-valued variational formulation in the spirit of [Y. Brenier. Comm. Math. Phys. (2018) 364(2) 579-605]. Employing time-adaptive weights,","authors_text":"Dmitry Vorotnikov","cross_cats":["math-ph","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-09T17:22:38Z","title":"Dafermos' principle and Brenier's duality scheme for defocusing dispersive equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05389","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":"sha256:95326e9e1f0a6921a2e06cc3049bebbfc7a9fbb37c731c10f9774010a680852c","target":"record","created_at":"2026-07-05T10:41:51Z","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":"99a354231f31aab66ec88706885a7e0b3f55674742ac937bf0329a6529668e1a","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-09T17:22:38Z","title_canon_sha256":"13835dd61631cb0143d7c6cbbc2dbbdec37de4edb0ee743a696460000a6f6b84"},"schema_version":"1.0","source":{"id":"2501.05389","kind":"arxiv","version":2}},"canonical_sha256":"3ddd7f9dc0fea7a085e6751a4b3a6455b232a7a0f3fe7cd6351e5d23621d6976","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ddd7f9dc0fea7a085e6751a4b3a6455b232a7a0f3fe7cd6351e5d23621d6976","first_computed_at":"2026-07-05T10:41:51.745435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:51.745435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W+deERlPZkeE9mRum3sRPXrniP7p6kZ8F9Tk+H5A6GiSiDh6HURQPFSb8cAbLX2rrQYb8K/G2C0N1s+nJO4gBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:51.745861Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.05389","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95326e9e1f0a6921a2e06cc3049bebbfc7a9fbb37c731c10f9774010a680852c","sha256:d70cef9955d3ceebdaef86e0df86ff340cc1f5d009bc74b004f866bd8dfac86f"],"state_sha256":"2ab8e998191ea0ae0534e14c9ba3f478e92b1b1258091eff86e5557f60d95002"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TKJ5BpZTQc21QGiDpiUevUwDkrpdTbEn9V2c+QxL3HyOJ6L+na/NzzfPTspmA/GtvAh9WMB4LTlhND2IvRJXDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T06:59:53.867893Z","bundle_sha256":"d5d5d4ed12c81eab5b036b6c135016fbc6692b25732323e922f5826351d0c1c8"}}