{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TPTX2VELT4B5WWQ66224YIPIKV","short_pith_number":"pith:TPTX2VEL","canonical_record":{"source":{"id":"1011.1737","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-11-08T09:20:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"dff8b7dd2db831ac8fdd998eba9d448f777873ca9eff202a09322c59bef93fbb","abstract_canon_sha256":"28a1245b51eaf5b89c8fbc61ed166e912aa51826138fd9d2fefb74a2f1f1b417"},"schema_version":"1.0"},"canonical_sha256":"9be77d548b9f03db5a1ef6b5cc21e855458edc26f95b31ac728bfef701f539e3","source":{"kind":"arxiv","id":"1011.1737","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1737","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1737v1","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1737","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"pith_short_12","alias_value":"TPTX2VELT4B5","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TPTX2VELT4B5WWQ6","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TPTX2VEL","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TPTX2VELT4B5WWQ66224YIPIKV","target":"record","payload":{"canonical_record":{"source":{"id":"1011.1737","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-11-08T09:20:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"dff8b7dd2db831ac8fdd998eba9d448f777873ca9eff202a09322c59bef93fbb","abstract_canon_sha256":"28a1245b51eaf5b89c8fbc61ed166e912aa51826138fd9d2fefb74a2f1f1b417"},"schema_version":"1.0"},"canonical_sha256":"9be77d548b9f03db5a1ef6b5cc21e855458edc26f95b31ac728bfef701f539e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:50.649426Z","signature_b64":"Gsp3h6TPKOz2QA/tILkJQYhXTsdarGF56cCfH92lrB3LHeDjEeAsH/O/nwsYaBqBoK9M24qEPBbyhrp4hseODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9be77d548b9f03db5a1ef6b5cc21e855458edc26f95b31ac728bfef701f539e3","last_reissued_at":"2026-05-18T04:36:50.648665Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:50.648665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.1737","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":"2026-05-18T04:36:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"12GoV01a6Crx5xFZwBy6PoN9giE2zCZoK2p51mKIISqN6rRF16nZvBsgbbGAIl2nErKh8Gi6ILiwPz9BYv4ZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:39:42.393389Z"},"content_sha256":"df3689517af000146a73ffffd910536c34ff74f9ea9a5a2b89d786c59a4ff7bc","schema_version":"1.0","event_id":"sha256:df3689517af000146a73ffffd910536c34ff74f9ea9a5a2b89d786c59a4ff7bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TPTX2VELT4B5WWQ66224YIPIKV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bidifferential calculus, matrix SIT and sine-Gordon equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Aristophanes Dimakis, Folkert Mueller-Hoissen, Nils Kanning","submitted_at":"2010-11-08T09:20:56Z","abstract_excerpt":"We express a matrix version of the self-induced transparency (SIT) equations in the bidifferential calculus framework. An infinite family of exact solutions is then obtained by application of a general result that generates exact solutions from solutions of a linear system of arbitrary matrix size. A side result is a solution formula for the sine-Gordon equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1737","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":"2026-05-18T04:36:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1LkJryc6L9P0q/7o5reZX6VsON5e8spdKV8drwI3Wwvnu8LHeq65CMA0GrevGLx60Gk/O2rvRleOPM7/hTeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:39:42.394106Z"},"content_sha256":"3ba977b9470735f208b1de0d33826b21b89fde72eca3a2e01aa4bcdfb9870d5f","schema_version":"1.0","event_id":"sha256:3ba977b9470735f208b1de0d33826b21b89fde72eca3a2e01aa4bcdfb9870d5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TPTX2VELT4B5WWQ66224YIPIKV/bundle.json","state_url":"https://pith.science/pith/TPTX2VELT4B5WWQ66224YIPIKV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TPTX2VELT4B5WWQ66224YIPIKV/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":"2026-06-11T22:39:42Z","links":{"resolver":"https://pith.science/pith/TPTX2VELT4B5WWQ66224YIPIKV","bundle":"https://pith.science/pith/TPTX2VELT4B5WWQ66224YIPIKV/bundle.json","state":"https://pith.science/pith/TPTX2VELT4B5WWQ66224YIPIKV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TPTX2VELT4B5WWQ66224YIPIKV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TPTX2VELT4B5WWQ66224YIPIKV","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":"28a1245b51eaf5b89c8fbc61ed166e912aa51826138fd9d2fefb74a2f1f1b417","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-11-08T09:20:56Z","title_canon_sha256":"dff8b7dd2db831ac8fdd998eba9d448f777873ca9eff202a09322c59bef93fbb"},"schema_version":"1.0","source":{"id":"1011.1737","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1737","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1737v1","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1737","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"pith_short_12","alias_value":"TPTX2VELT4B5","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TPTX2VELT4B5WWQ6","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TPTX2VEL","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:3ba977b9470735f208b1de0d33826b21b89fde72eca3a2e01aa4bcdfb9870d5f","target":"graph","created_at":"2026-05-18T04:36:50Z","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 express a matrix version of the self-induced transparency (SIT) equations in the bidifferential calculus framework. An infinite family of exact solutions is then obtained by application of a general result that generates exact solutions from solutions of a linear system of arbitrary matrix size. A side result is a solution formula for the sine-Gordon equation.","authors_text":"Aristophanes Dimakis, Folkert Mueller-Hoissen, Nils Kanning","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-11-08T09:20:56Z","title":"Bidifferential calculus, matrix SIT and sine-Gordon equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1737","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:df3689517af000146a73ffffd910536c34ff74f9ea9a5a2b89d786c59a4ff7bc","target":"record","created_at":"2026-05-18T04:36:50Z","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":"28a1245b51eaf5b89c8fbc61ed166e912aa51826138fd9d2fefb74a2f1f1b417","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-11-08T09:20:56Z","title_canon_sha256":"dff8b7dd2db831ac8fdd998eba9d448f777873ca9eff202a09322c59bef93fbb"},"schema_version":"1.0","source":{"id":"1011.1737","kind":"arxiv","version":1}},"canonical_sha256":"9be77d548b9f03db5a1ef6b5cc21e855458edc26f95b31ac728bfef701f539e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9be77d548b9f03db5a1ef6b5cc21e855458edc26f95b31ac728bfef701f539e3","first_computed_at":"2026-05-18T04:36:50.648665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:50.648665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gsp3h6TPKOz2QA/tILkJQYhXTsdarGF56cCfH92lrB3LHeDjEeAsH/O/nwsYaBqBoK9M24qEPBbyhrp4hseODw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:50.649426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df3689517af000146a73ffffd910536c34ff74f9ea9a5a2b89d786c59a4ff7bc","sha256:3ba977b9470735f208b1de0d33826b21b89fde72eca3a2e01aa4bcdfb9870d5f"],"state_sha256":"d671e25b34ecc270db2cd11b322e9a584cf63d66778ff09c0982b08230504f61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uA9132eFjA5RS6DkK7J8/USTQjeRf0TCMqQAko6Vs/AWOGbkudJyS/bOXDv07J7+vjPlsXV1gUSZcW01Bw+wAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:39:42.397940Z","bundle_sha256":"3cc1005da44773caa8dfcf22feab39ee3925d33ba27fee14f84cfaacb535b2b1"}}