{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VB4YJ72522EUM7KTCGFSENMX4P","short_pith_number":"pith:VB4YJ725","canonical_record":{"source":{"id":"1307.1780","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-06T13:26:09Z","cross_cats_sorted":["hep-th","math.AP","math.MP"],"title_canon_sha256":"ab4ed1b75209f226a3314eb1bff0b614ec1656829bc80ea94a0ba697003eb986","abstract_canon_sha256":"42e3a87d5a71873f8eaacd187dd03231c625ae859703d1f82ed5a7b4857785b6"},"schema_version":"1.0"},"canonical_sha256":"a87984ff5dd689467d53118b223597e3dca740e649ff7a9c88e935be8df50819","source":{"kind":"arxiv","id":"1307.1780","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1780","created_at":"2026-07-05T03:13:59Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1780v2","created_at":"2026-07-05T03:13:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1780","created_at":"2026-07-05T03:13:59Z"},{"alias_kind":"pith_short_12","alias_value":"VB4YJ72522EU","created_at":"2026-07-05T03:13:59Z"},{"alias_kind":"pith_short_16","alias_value":"VB4YJ72522EUM7KT","created_at":"2026-07-05T03:13:59Z"},{"alias_kind":"pith_short_8","alias_value":"VB4YJ725","created_at":"2026-07-05T03:13:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VB4YJ72522EUM7KTCGFSENMX4P","target":"record","payload":{"canonical_record":{"source":{"id":"1307.1780","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-06T13:26:09Z","cross_cats_sorted":["hep-th","math.AP","math.MP"],"title_canon_sha256":"ab4ed1b75209f226a3314eb1bff0b614ec1656829bc80ea94a0ba697003eb986","abstract_canon_sha256":"42e3a87d5a71873f8eaacd187dd03231c625ae859703d1f82ed5a7b4857785b6"},"schema_version":"1.0"},"canonical_sha256":"a87984ff5dd689467d53118b223597e3dca740e649ff7a9c88e935be8df50819","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:13:59.414701Z","signature_b64":"UfTvSKlINV8HUDtqFM8B/7EZiqkeGpz41LlAPjkNqQzWybJo2K2d/18LCQqQ0VMCRQqjUuF2h0KZoqjEghywAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a87984ff5dd689467d53118b223597e3dca740e649ff7a9c88e935be8df50819","last_reissued_at":"2026-07-05T03:13:59.414287Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:13:59.414287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.1780","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":"2026-07-05T03:13:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"66shn10zZl3diCeMGFkT57S2jTub/MrqPNIzBIHvtf192jUml4dCoY2L0KGTSHxVq2pX9yJaPAZweRjkX75LBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:30:52.551490Z"},"content_sha256":"fced2c43872747a81ee0b3028e7b93db680ed28d23629bc5cf19546b217c5726","schema_version":"1.0","event_id":"sha256:fced2c43872747a81ee0b3028e7b93db680ed28d23629bc5cf19546b217c5726"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VB4YJ72522EUM7KTCGFSENMX4P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear hyperbolic PDEs with non-commutative time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Gandalf Lechner, Rainer Verch","submitted_at":"2013-07-06T13:26:09Z","abstract_excerpt":"Motivated by wave or Dirac equations on noncommutative deformations of Minkowski space, linear integro-differential equations of the form $(D+\\lambda W)f=0$ are studied, where $D$ is a normal or prenormal hyperbolic differential operator on ${\\mathbb R}^n$, $\\lambda\\in\\mathbb C$ is a coupling constant, and $W$ is a regular integral operator with compactly supported kernel. In particular, $W$ can be non-local in time, so that a Hamiltonian formulation is not possible. It is shown that for sufficiently small $|\\lambda|$, the hyperbolic character of $D$ is essentially preserved. Unique advanced/r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1780","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/1307.1780/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":"2026-07-05T03:13:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IFr3xgj/pWguEp5UE21lbEXjhe9C+00et7JTUZb5JOvv1QuX+1X71V09MgkNoMaOccoFPz2zvKHM0i2xt+baCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:30:52.552007Z"},"content_sha256":"a52596776a082d0d8e3dc3fb925ff763fd1fc4e8870033e9c1e9b3a241c5605e","schema_version":"1.0","event_id":"sha256:a52596776a082d0d8e3dc3fb925ff763fd1fc4e8870033e9c1e9b3a241c5605e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VB4YJ72522EUM7KTCGFSENMX4P/bundle.json","state_url":"https://pith.science/pith/VB4YJ72522EUM7KTCGFSENMX4P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VB4YJ72522EUM7KTCGFSENMX4P/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":"2026-08-10T19:30:52Z","links":{"resolver":"https://pith.science/pith/VB4YJ72522EUM7KTCGFSENMX4P","bundle":"https://pith.science/pith/VB4YJ72522EUM7KTCGFSENMX4P/bundle.json","state":"https://pith.science/pith/VB4YJ72522EUM7KTCGFSENMX4P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VB4YJ72522EUM7KTCGFSENMX4P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VB4YJ72522EUM7KTCGFSENMX4P","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":"42e3a87d5a71873f8eaacd187dd03231c625ae859703d1f82ed5a7b4857785b6","cross_cats_sorted":["hep-th","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-06T13:26:09Z","title_canon_sha256":"ab4ed1b75209f226a3314eb1bff0b614ec1656829bc80ea94a0ba697003eb986"},"schema_version":"1.0","source":{"id":"1307.1780","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1780","created_at":"2026-07-05T03:13:59Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1780v2","created_at":"2026-07-05T03:13:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1780","created_at":"2026-07-05T03:13:59Z"},{"alias_kind":"pith_short_12","alias_value":"VB4YJ72522EU","created_at":"2026-07-05T03:13:59Z"},{"alias_kind":"pith_short_16","alias_value":"VB4YJ72522EUM7KT","created_at":"2026-07-05T03:13:59Z"},{"alias_kind":"pith_short_8","alias_value":"VB4YJ725","created_at":"2026-07-05T03:13:59Z"}],"graph_snapshots":[{"event_id":"sha256:a52596776a082d0d8e3dc3fb925ff763fd1fc4e8870033e9c1e9b3a241c5605e","target":"graph","created_at":"2026-07-05T03:13:59Z","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/1307.1780/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by wave or Dirac equations on noncommutative deformations of Minkowski space, linear integro-differential equations of the form $(D+\\lambda W)f=0$ are studied, where $D$ is a normal or prenormal hyperbolic differential operator on ${\\mathbb R}^n$, $\\lambda\\in\\mathbb C$ is a coupling constant, and $W$ is a regular integral operator with compactly supported kernel. In particular, $W$ can be non-local in time, so that a Hamiltonian formulation is not possible. It is shown that for sufficiently small $|\\lambda|$, the hyperbolic character of $D$ is essentially preserved. Unique advanced/r","authors_text":"Gandalf Lechner, Rainer Verch","cross_cats":["hep-th","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-06T13:26:09Z","title":"Linear hyperbolic PDEs with non-commutative time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1780","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:fced2c43872747a81ee0b3028e7b93db680ed28d23629bc5cf19546b217c5726","target":"record","created_at":"2026-07-05T03:13:59Z","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":"42e3a87d5a71873f8eaacd187dd03231c625ae859703d1f82ed5a7b4857785b6","cross_cats_sorted":["hep-th","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-06T13:26:09Z","title_canon_sha256":"ab4ed1b75209f226a3314eb1bff0b614ec1656829bc80ea94a0ba697003eb986"},"schema_version":"1.0","source":{"id":"1307.1780","kind":"arxiv","version":2}},"canonical_sha256":"a87984ff5dd689467d53118b223597e3dca740e649ff7a9c88e935be8df50819","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a87984ff5dd689467d53118b223597e3dca740e649ff7a9c88e935be8df50819","first_computed_at":"2026-07-05T03:13:59.414287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:13:59.414287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UfTvSKlINV8HUDtqFM8B/7EZiqkeGpz41LlAPjkNqQzWybJo2K2d/18LCQqQ0VMCRQqjUuF2h0KZoqjEghywAA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:13:59.414701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1780","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fced2c43872747a81ee0b3028e7b93db680ed28d23629bc5cf19546b217c5726","sha256:a52596776a082d0d8e3dc3fb925ff763fd1fc4e8870033e9c1e9b3a241c5605e"],"state_sha256":"950c12604902cdacdd82743cf8e7ba8d493ee46a438dc39909a7d6d18c1fbbe7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N3/OzA9AYDu6pRLi/b+fCa23ocX6Ief9RoQni1oUGBotJN/yPFXR61hY+5GD5EQfaM2B+NxxSqZqBltVSuhRBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T19:30:52.556489Z","bundle_sha256":"aa26e47390b8f7b93b1c5db987fa6a6910ab33face3a3afeae0aae8b1bbce66d"}}