{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UJNLDJCR4BGVRJQRAI3DGQERAU","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":"368a69676c486e82fd3507cbd9c8be7d34c0a285c23d61bf24794d9d15f426c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-07T21:59:31Z","title_canon_sha256":"af69c43ceab4627c73fd7200f195a92866651f1e0e722120ed467632027f50d2"},"schema_version":"1.0","source":{"id":"1509.02204","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02204","created_at":"2026-05-18T01:18:43Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02204v2","created_at":"2026-05-18T01:18:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02204","created_at":"2026-05-18T01:18:43Z"},{"alias_kind":"pith_short_12","alias_value":"UJNLDJCR4BGV","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UJNLDJCR4BGVRJQR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UJNLDJCR","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:c039bc1bc734ad8142c278f9c53ba20289d1aa3dbf99d16286b72da808831f87","target":"graph","created_at":"2026-05-18T01:18:43Z","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 study an undirected polymer chain living on the 1-dimensional integer lattice and carrying i.i.d.\\ random charges. Each self-intersection of the polymer contributes to the Hamiltonian an energy that is equal to the product of the charges of the two monomers that meet. The joint law for the polymer chain and the charges is given by the Gibbs distribution associated with the Hamiltonian. The focus is on the \\emph{annealed free energy} per monomer in the limit as polymer length diverges.\n  We derive a \\emph{spectral representation} for the free energy and we exhibit a critical curve in the par","authors_text":"F. Caravenna, F. den Hollander, J. Poisat, N. P\\'etr\\'elis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-07T21:59:31Z","title":"Annealed scaling for a charged polymer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02204","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:f4e9facca7aeb7b5f8c320145e7695d2380bab0f1c9e2aff5f13214f9a7a8887","target":"record","created_at":"2026-05-18T01:18:43Z","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":"368a69676c486e82fd3507cbd9c8be7d34c0a285c23d61bf24794d9d15f426c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-07T21:59:31Z","title_canon_sha256":"af69c43ceab4627c73fd7200f195a92866651f1e0e722120ed467632027f50d2"},"schema_version":"1.0","source":{"id":"1509.02204","kind":"arxiv","version":2}},"canonical_sha256":"a25ab1a451e04d58a6110236334091051cf69ddcb64753d2e591db9cfecd2dea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a25ab1a451e04d58a6110236334091051cf69ddcb64753d2e591db9cfecd2dea","first_computed_at":"2026-05-18T01:18:43.232294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:43.232294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mf1A8CxVPecTtsMA0Ym5q3KT9jlQr9YNyPn/SsWn8vhA3tkyrj5TOOCuhxiQ2pMZ86s9qOuuDOaqFutTQoNoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:43.232999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02204","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4e9facca7aeb7b5f8c320145e7695d2380bab0f1c9e2aff5f13214f9a7a8887","sha256:c039bc1bc734ad8142c278f9c53ba20289d1aa3dbf99d16286b72da808831f87"],"state_sha256":"9c0ef4cd2ee1c1a36b67b5f109320530cac403534bfe55ce800b84bdbdd51f9d"}