{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:G2BCCF4WOIBB4CW5G7HER3L7M2","short_pith_number":"pith:G2BCCF4W","canonical_record":{"source":{"id":"1308.2060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-09T09:26:29Z","cross_cats_sorted":[],"title_canon_sha256":"c6b6a22b4ed0a30a1842176d8bd48306ba454023aaad2b54a9d2ac7873496b6d","abstract_canon_sha256":"a29193abb30720c35e819746612ec3c8c9df9334f8958a5e62177e29aa5e6507"},"schema_version":"1.0"},"canonical_sha256":"368221179672021e0add37ce48ed7f66b5b07395d88da780df1aefe7ee29b39a","source":{"kind":"arxiv","id":"1308.2060","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2060","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2060v1","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2060","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"pith_short_12","alias_value":"G2BCCF4WOIBB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G2BCCF4WOIBB4CW5","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G2BCCF4W","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:G2BCCF4WOIBB4CW5G7HER3L7M2","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-09T09:26:29Z","cross_cats_sorted":[],"title_canon_sha256":"c6b6a22b4ed0a30a1842176d8bd48306ba454023aaad2b54a9d2ac7873496b6d","abstract_canon_sha256":"a29193abb30720c35e819746612ec3c8c9df9334f8958a5e62177e29aa5e6507"},"schema_version":"1.0"},"canonical_sha256":"368221179672021e0add37ce48ed7f66b5b07395d88da780df1aefe7ee29b39a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:18.337343Z","signature_b64":"khBc3cWvuILIOneW6O0wsCYxhDV0zSGqki8FdtYZRhAap0VRjsjZkx3Rb/ivFbZbCbeG1NFOTpbdfxUzoPbYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"368221179672021e0add37ce48ed7f66b5b07395d88da780df1aefe7ee29b39a","last_reissued_at":"2026-05-18T03:16:18.336420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:18.336420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2060","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":"2026-05-18T03:16:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KzW1W1A87hIa9jl9TdbmM9s2DcgZovtGEa75qzvLc+RI9rcwCyPvWn10nPJ3Jb7vTcUAWa1POHYOzc8SCzDNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:06:04.367926Z"},"content_sha256":"cb2381f1ae3fe69fa45bece7bf45e8b5f9c8ee66e7873702ccad03ff43468a05","schema_version":"1.0","event_id":"sha256:cb2381f1ae3fe69fa45bece7bf45e8b5f9c8ee66e7873702ccad03ff43468a05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:G2BCCF4WOIBB4CW5G7HER3L7M2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Longtime behavior of coupled wave equations for semiconductor lasers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jan Sieber","submitted_at":"2013-08-09T09:26:29Z","abstract_excerpt":"Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial differential equations with one spatial dimension, which is nonlinearly coupled with a slow subsystem of ordinary differential equations. We first prove the basic statements about the existence of solutions of the initial-boundary-value problem and their smooth dependence on initial values and parameters. Hence, the model constitutes a smooth infinite-dimens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2060","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":"2026-05-18T03:16:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uhCa4sq/cwfJyJTuopPLYxd16kXIYRxgnh7mRMFxbgYTKvUfeWZhSTNMQb/tXrMG+nExehPmZhUfPx/BRE4dBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:06:04.368458Z"},"content_sha256":"2de20365c9ab85a8bafef75f0e3d20f1ded38fe452f597cd706182368e804b21","schema_version":"1.0","event_id":"sha256:2de20365c9ab85a8bafef75f0e3d20f1ded38fe452f597cd706182368e804b21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G2BCCF4WOIBB4CW5G7HER3L7M2/bundle.json","state_url":"https://pith.science/pith/G2BCCF4WOIBB4CW5G7HER3L7M2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G2BCCF4WOIBB4CW5G7HER3L7M2/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":"2026-05-27T13:06:04Z","links":{"resolver":"https://pith.science/pith/G2BCCF4WOIBB4CW5G7HER3L7M2","bundle":"https://pith.science/pith/G2BCCF4WOIBB4CW5G7HER3L7M2/bundle.json","state":"https://pith.science/pith/G2BCCF4WOIBB4CW5G7HER3L7M2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G2BCCF4WOIBB4CW5G7HER3L7M2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:G2BCCF4WOIBB4CW5G7HER3L7M2","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":"a29193abb30720c35e819746612ec3c8c9df9334f8958a5e62177e29aa5e6507","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-09T09:26:29Z","title_canon_sha256":"c6b6a22b4ed0a30a1842176d8bd48306ba454023aaad2b54a9d2ac7873496b6d"},"schema_version":"1.0","source":{"id":"1308.2060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2060","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2060v1","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2060","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"pith_short_12","alias_value":"G2BCCF4WOIBB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G2BCCF4WOIBB4CW5","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G2BCCF4W","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:2de20365c9ab85a8bafef75f0e3d20f1ded38fe452f597cd706182368e804b21","target":"graph","created_at":"2026-05-18T03:16:18Z","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":"Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial differential equations with one spatial dimension, which is nonlinearly coupled with a slow subsystem of ordinary differential equations. We first prove the basic statements about the existence of solutions of the initial-boundary-value problem and their smooth dependence on initial values and parameters. Hence, the model constitutes a smooth infinite-dimens","authors_text":"Jan Sieber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-09T09:26:29Z","title":"Longtime behavior of coupled wave equations for semiconductor lasers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2060","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:cb2381f1ae3fe69fa45bece7bf45e8b5f9c8ee66e7873702ccad03ff43468a05","target":"record","created_at":"2026-05-18T03:16:18Z","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":"a29193abb30720c35e819746612ec3c8c9df9334f8958a5e62177e29aa5e6507","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-09T09:26:29Z","title_canon_sha256":"c6b6a22b4ed0a30a1842176d8bd48306ba454023aaad2b54a9d2ac7873496b6d"},"schema_version":"1.0","source":{"id":"1308.2060","kind":"arxiv","version":1}},"canonical_sha256":"368221179672021e0add37ce48ed7f66b5b07395d88da780df1aefe7ee29b39a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"368221179672021e0add37ce48ed7f66b5b07395d88da780df1aefe7ee29b39a","first_computed_at":"2026-05-18T03:16:18.336420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:18.336420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"khBc3cWvuILIOneW6O0wsCYxhDV0zSGqki8FdtYZRhAap0VRjsjZkx3Rb/ivFbZbCbeG1NFOTpbdfxUzoPbYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:18.337343Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb2381f1ae3fe69fa45bece7bf45e8b5f9c8ee66e7873702ccad03ff43468a05","sha256:2de20365c9ab85a8bafef75f0e3d20f1ded38fe452f597cd706182368e804b21"],"state_sha256":"e52644c0f4102ab62e8591587a9e5b2da5890a20ad4719ee36f9897ca4e24c60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YH6pAbhS70+IxKPpa3cjY7Xhtz2djdp2/2AacWtWLPM+1ltU7DDUMlCM6UM7cu694GFGfntMS1DGGyNzONz0AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:06:04.371434Z","bundle_sha256":"8c8f7bdfea423b79003a93f027891c018bdfb35494db172badbae13a71a0e9da"}}