{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:T4UDLZMXQA4PLHYN4CEKKTPVO5","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":"1012c7c01ed39919fb72270afcea01def08650be79ae45759fb535ffc23baf17","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-18T18:07:44Z","title_canon_sha256":"767de0df0d355a665dfd9d49679623c2a993a21aaf2a81670dffc955267ad2c7"},"schema_version":"1.0","source":{"id":"2606.20821","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20821","created_at":"2026-06-23T00:11:59Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20821v1","created_at":"2026-06-23T00:11:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20821","created_at":"2026-06-23T00:11:59Z"},{"alias_kind":"pith_short_12","alias_value":"T4UDLZMXQA4P","created_at":"2026-06-23T00:11:59Z"},{"alias_kind":"pith_short_16","alias_value":"T4UDLZMXQA4PLHYN","created_at":"2026-06-23T00:11:59Z"},{"alias_kind":"pith_short_8","alias_value":"T4UDLZMX","created_at":"2026-06-23T00:11:59Z"}],"graph_snapshots":[{"event_id":"sha256:cf79061a02e722c152c1509e3aab3f547e3c07ff88c189743048beceb72a6e79","target":"graph","created_at":"2026-06-23T00:11:59Z","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/2606.20821/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a nonlinear Helmholtz system with cubic nonlinearity on high-contrast inclusions in three dimensions, and the solitons that emerge as the contrast $\\delta$ tends to zero. Using the Dirichlet-to-Neumann operator and a capacitance formalism, we develop a perturbative cascade that expands the resonant frequency and field in powers of $\\sqrt{\\delta}$. Our main result is a rigorous two-way correspondence with a finite discrete nonlinear capacitance system: every discrete solution lifts to a continuous soliton (a convergent expansion, analytic in $\\sqrt{\\delta}$), and every continuous famil","authors_text":"Clemens Thalhammer, Habib Ammari","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-18T18:07:44Z","title":"Perturbative Approach to Nonlinear Capacitance Matrix Formulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20821","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:e6bd4beed83bdf078085e81ff42b719f82c08b10f6c51c2905b7dd192e596af9","target":"record","created_at":"2026-06-23T00:11:59Z","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":"1012c7c01ed39919fb72270afcea01def08650be79ae45759fb535ffc23baf17","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-18T18:07:44Z","title_canon_sha256":"767de0df0d355a665dfd9d49679623c2a993a21aaf2a81670dffc955267ad2c7"},"schema_version":"1.0","source":{"id":"2606.20821","kind":"arxiv","version":1}},"canonical_sha256":"9f2835e5978038f59f0de088a54df577746f7e3e5126734160609cba80f55756","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f2835e5978038f59f0de088a54df577746f7e3e5126734160609cba80f55756","first_computed_at":"2026-06-23T00:11:59.721235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T00:11:59.721235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bWxGOE1HMJuDHqFhi6l9IDzY5HPOiBSb1ySB0Gg6nCMklZfswNT4YjDjsBUGgGpj+YFCo98Zciyp9BKXlISAAg==","signature_status":"signed_v1","signed_at":"2026-06-23T00:11:59.721637Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.20821","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6bd4beed83bdf078085e81ff42b719f82c08b10f6c51c2905b7dd192e596af9","sha256:cf79061a02e722c152c1509e3aab3f547e3c07ff88c189743048beceb72a6e79"],"state_sha256":"c15e0a4fb6498765c34cf3e9eb188f5fa6011fafb1f40c202c93ce477b0c9e60"}