{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5ZSSGRLTLEUDSXTGCYLDHMNPAR","short_pith_number":"pith:5ZSSGRLT","canonical_record":{"source":{"id":"1412.4164","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2014-12-12T23:38:31Z","cross_cats_sorted":[],"title_canon_sha256":"ce0acbd2c5ea9449f9cc7fb68ce11a4bad3ec5976ba7c772a5bd919692151418","abstract_canon_sha256":"0f1ef6ffdb0129b122f00e175b0c48ced086205c630189d50adc54ec1c76ed4b"},"schema_version":"1.0"},"canonical_sha256":"ee652345735928395e66161633b1af045b61d44f3e7d64920459b1c27fda8175","source":{"kind":"arxiv","id":"1412.4164","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4164","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4164v2","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4164","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"pith_short_12","alias_value":"5ZSSGRLTLEUD","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5ZSSGRLTLEUDSXTG","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5ZSSGRLT","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5ZSSGRLTLEUDSXTGCYLDHMNPAR","target":"record","payload":{"canonical_record":{"source":{"id":"1412.4164","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2014-12-12T23:38:31Z","cross_cats_sorted":[],"title_canon_sha256":"ce0acbd2c5ea9449f9cc7fb68ce11a4bad3ec5976ba7c772a5bd919692151418","abstract_canon_sha256":"0f1ef6ffdb0129b122f00e175b0c48ced086205c630189d50adc54ec1c76ed4b"},"schema_version":"1.0"},"canonical_sha256":"ee652345735928395e66161633b1af045b61d44f3e7d64920459b1c27fda8175","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:05.482018Z","signature_b64":"81G2mMrCLZ8apekcEUjwpDd5Zh8QD6uR5pir88PiHkvnmpXIMYtNKolQAogy0kZFCOfAyQXP0n33KXEfm1NsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee652345735928395e66161633b1af045b61d44f3e7d64920459b1c27fda8175","last_reissued_at":"2026-05-18T01:27:05.481288Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:05.481288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.4164","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":"2026-05-18T01:27:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QOJPehjSJ9vzb2fMML3CxCoN5O6zwxRfl0xZk7cZQRHM/dfvD6EoaSLl6wzmoFAfW4+7gAW3l9aZpENivAxuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:58:29.381670Z"},"content_sha256":"0e220f70856582b77fe40acb1b275fa5147cd1f3dbce6892520b6dd3c5c1ca74","schema_version":"1.0","event_id":"sha256:0e220f70856582b77fe40acb1b275fa5147cd1f3dbce6892520b6dd3c5c1ca74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5ZSSGRLTLEUDSXTGCYLDHMNPAR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Closed-form solutions and scaling laws for Kerr frequency combs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Peter T. Rakich, William H. Renninger","submitted_at":"2014-12-12T23:38:31Z","abstract_excerpt":"A single closed-form analytical solution of the driven nonlinear Schr\\\"{o}dinger equation is developed, reproducing a large class of the behaviors in Kerr-comb systems, including bright-solitons, dark-solitons, and a large class of periodic wavetrains. From this analytical framework, a Kerr-comb area theorem and a pump-detuning relation are developed, providing new insights into soliton- and wavetrain-based combs along with concrete design guidelines for both. This new area theorem reveals significant deviation from the conventional soliton area theorem, which is crucial to understanding cavit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4164","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":""},"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":"2026-05-18T01:27:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RS3HWEXsC//RSL2qQCP2u6rDGXDsapuXHQ02w/NVIj5jutfb276uTZ9GaOu/Is6X7Yi9sxF3sG52d2TvlcM0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:58:29.382338Z"},"content_sha256":"09c7f3e3ca418f41ebcf9cd5af6ed95a46ae45fc6d60445eeb0eb3868cc4aab4","schema_version":"1.0","event_id":"sha256:09c7f3e3ca418f41ebcf9cd5af6ed95a46ae45fc6d60445eeb0eb3868cc4aab4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ZSSGRLTLEUDSXTGCYLDHMNPAR/bundle.json","state_url":"https://pith.science/pith/5ZSSGRLTLEUDSXTGCYLDHMNPAR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ZSSGRLTLEUDSXTGCYLDHMNPAR/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":"2026-06-11T00:58:29Z","links":{"resolver":"https://pith.science/pith/5ZSSGRLTLEUDSXTGCYLDHMNPAR","bundle":"https://pith.science/pith/5ZSSGRLTLEUDSXTGCYLDHMNPAR/bundle.json","state":"https://pith.science/pith/5ZSSGRLTLEUDSXTGCYLDHMNPAR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ZSSGRLTLEUDSXTGCYLDHMNPAR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5ZSSGRLTLEUDSXTGCYLDHMNPAR","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":"0f1ef6ffdb0129b122f00e175b0c48ced086205c630189d50adc54ec1c76ed4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2014-12-12T23:38:31Z","title_canon_sha256":"ce0acbd2c5ea9449f9cc7fb68ce11a4bad3ec5976ba7c772a5bd919692151418"},"schema_version":"1.0","source":{"id":"1412.4164","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4164","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4164v2","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4164","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"pith_short_12","alias_value":"5ZSSGRLTLEUD","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5ZSSGRLTLEUDSXTG","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5ZSSGRLT","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:09c7f3e3ca418f41ebcf9cd5af6ed95a46ae45fc6d60445eeb0eb3868cc4aab4","target":"graph","created_at":"2026-05-18T01:27:05Z","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":"A single closed-form analytical solution of the driven nonlinear Schr\\\"{o}dinger equation is developed, reproducing a large class of the behaviors in Kerr-comb systems, including bright-solitons, dark-solitons, and a large class of periodic wavetrains. From this analytical framework, a Kerr-comb area theorem and a pump-detuning relation are developed, providing new insights into soliton- and wavetrain-based combs along with concrete design guidelines for both. This new area theorem reveals significant deviation from the conventional soliton area theorem, which is crucial to understanding cavit","authors_text":"Peter T. Rakich, William H. Renninger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2014-12-12T23:38:31Z","title":"Closed-form solutions and scaling laws for Kerr frequency combs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4164","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":"sha256:0e220f70856582b77fe40acb1b275fa5147cd1f3dbce6892520b6dd3c5c1ca74","target":"record","created_at":"2026-05-18T01:27:05Z","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":"0f1ef6ffdb0129b122f00e175b0c48ced086205c630189d50adc54ec1c76ed4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2014-12-12T23:38:31Z","title_canon_sha256":"ce0acbd2c5ea9449f9cc7fb68ce11a4bad3ec5976ba7c772a5bd919692151418"},"schema_version":"1.0","source":{"id":"1412.4164","kind":"arxiv","version":2}},"canonical_sha256":"ee652345735928395e66161633b1af045b61d44f3e7d64920459b1c27fda8175","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee652345735928395e66161633b1af045b61d44f3e7d64920459b1c27fda8175","first_computed_at":"2026-05-18T01:27:05.481288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:05.481288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"81G2mMrCLZ8apekcEUjwpDd5Zh8QD6uR5pir88PiHkvnmpXIMYtNKolQAogy0kZFCOfAyQXP0n33KXEfm1NsBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:05.482018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4164","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e220f70856582b77fe40acb1b275fa5147cd1f3dbce6892520b6dd3c5c1ca74","sha256:09c7f3e3ca418f41ebcf9cd5af6ed95a46ae45fc6d60445eeb0eb3868cc4aab4"],"state_sha256":"1e052885a165426974f3abd5be296dab8e3662b8e41a7ee3f3f91b3360791fa0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KDckHLHPLzrUQq+fD+Jove+wtR1VujnjGKUJBhy2Lfbemf+vVuzpdAKuDx1v413i++KJi6T5Fgt4zfBRYuunAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:58:29.385924Z","bundle_sha256":"758505faf866b4411ebacf6dd1998b736521d2be5baf03f52d956574a8676380"}}