{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7XNVLUHXSPIUYIHQGGUT4UNGLF","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":"32a6f9bd80da720757ca4b4aea91ad28bad4eec08d33aa9eb284b29fa78ad627","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-31T15:39:12Z","title_canon_sha256":"defa6a3f15deb7bcf44424a8a3d50a78aa567d89cd93ae40c25e6e9fd77848d0"},"schema_version":"1.0","source":{"id":"2407.21694","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.21694","created_at":"2026-07-05T08:50:42Z"},{"alias_kind":"arxiv_version","alias_value":"2407.21694v1","created_at":"2026-07-05T08:50:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.21694","created_at":"2026-07-05T08:50:42Z"},{"alias_kind":"pith_short_12","alias_value":"7XNVLUHXSPIU","created_at":"2026-07-05T08:50:42Z"},{"alias_kind":"pith_short_16","alias_value":"7XNVLUHXSPIUYIHQ","created_at":"2026-07-05T08:50:42Z"},{"alias_kind":"pith_short_8","alias_value":"7XNVLUHX","created_at":"2026-07-05T08:50:42Z"}],"graph_snapshots":[{"event_id":"sha256:9d5ad570af4b8d679ca0db50e30dadd1f15eaf05cc6091ee56cd4e0bfe4a7314","target":"graph","created_at":"2026-07-05T08:50:42Z","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/2407.21694/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Kramers-Kronig relations link the real and imaginary part of the Fourier transform of a well-behaved causal transfer function describing a linear, time-invariant system. From the physical point of view, according to the Kramers-Kronig relations, absorption and dispersion become two sides of the same coin. Due to the simplicity of the assumptions underlying them, the relations are a cornerstone of physics. The rigorous mathematical proof was carried out by Titchmarsh in 1937 and just requires the transfer function to be square-integrable ($L^2$), or equivalently that the impulse response of the","authors_text":"Alessio Perinelli, Leonardo Ricci, Marco Prevedelli","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-31T15:39:12Z","title":"Kramers-Kronig relations via Laplace formalism and $L^1$ integrability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.21694","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":"sha256:107da9e0ba5cb0cb9e9bc8dcfd696177597770d40be9e7800320e9e722cec68e","target":"record","created_at":"2026-07-05T08:50:42Z","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":"32a6f9bd80da720757ca4b4aea91ad28bad4eec08d33aa9eb284b29fa78ad627","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-31T15:39:12Z","title_canon_sha256":"defa6a3f15deb7bcf44424a8a3d50a78aa567d89cd93ae40c25e6e9fd77848d0"},"schema_version":"1.0","source":{"id":"2407.21694","kind":"arxiv","version":1}},"canonical_sha256":"fddb55d0f793d14c20f031a93e51a65945816fa494e66798a472015816beeaa0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fddb55d0f793d14c20f031a93e51a65945816fa494e66798a472015816beeaa0","first_computed_at":"2026-07-05T08:50:42.525853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:50:42.525853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aO3hsxOgcFMAXvDRmibskr3CstA3VYWEbLYizi2ufOsmz5ztRiy9Se1Ly4VMx2LekNbPEGKEN5BnDDadx4BTAA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:50:42.526382Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.21694","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:107da9e0ba5cb0cb9e9bc8dcfd696177597770d40be9e7800320e9e722cec68e","sha256:9d5ad570af4b8d679ca0db50e30dadd1f15eaf05cc6091ee56cd4e0bfe4a7314"],"state_sha256":"a1756361998b6b5e5128c58dbb46cb0f4250e39554932b946dd2711688897ecf"}