{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BFAOV6QPBDREUE7PSAPSNDETM5","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":"610fa5bd142c7e7ac5725621ef6d6fa07c21fdd573bd2f8501e69163f87638ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-01T16:54:22Z","title_canon_sha256":"9d30f64286af1142b9b908104ab20bfa3a820ae2acddea9dc795eefd10cc0158"},"schema_version":"1.0","source":{"id":"1103.0214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0214","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0214v1","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0214","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"pith_short_12","alias_value":"BFAOV6QPBDRE","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BFAOV6QPBDREUE7P","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BFAOV6QP","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:c574dee6b00a0f96bfb5f5d0a7cc49bc6eba9f799458905f04333c2dad2a4d6d","target":"graph","created_at":"2026-05-18T04:27:37Z","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 consider a random $N$-step polymer under the influence of an attractive interaction with the origin and derive a limit law -- after suitable shifting and norming -- for the length of the longest excursion towards the Gumbel distribution. The embodied law of large numbers in particular implies that the longest excursion is of order $\\log N$ long. The main tools are taken from extreme value theory and renewal theory.","authors_text":"Janine K\\\"ocher, Wolfgang K\\\"onig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-01T16:54:22Z","title":"The longest excursion of a random interacting polymer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0214","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":"sha256:095c8987554364b41cec1c0f0a59811126d439dfdf345ab09bef379172a21260","target":"record","created_at":"2026-05-18T04:27:37Z","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":"610fa5bd142c7e7ac5725621ef6d6fa07c21fdd573bd2f8501e69163f87638ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-01T16:54:22Z","title_canon_sha256":"9d30f64286af1142b9b908104ab20bfa3a820ae2acddea9dc795eefd10cc0158"},"schema_version":"1.0","source":{"id":"1103.0214","kind":"arxiv","version":1}},"canonical_sha256":"0940eafa0f08e24a13ef901f268c93676a4d758e6313639819ad71f926e67076","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0940eafa0f08e24a13ef901f268c93676a4d758e6313639819ad71f926e67076","first_computed_at":"2026-05-18T04:27:37.068393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:37.068393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G0NMH+LYJ/UeMnoOZdaaHm6R5nGS/gbegW1ykq9vhHTRTDoJrRCZ3cCDiKYm8EOQKobfoiJKgCtBmfWhaL9nCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:37.069033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:095c8987554364b41cec1c0f0a59811126d439dfdf345ab09bef379172a21260","sha256:c574dee6b00a0f96bfb5f5d0a7cc49bc6eba9f799458905f04333c2dad2a4d6d"],"state_sha256":"1b1904ca238b7ccfd12d52306c2e10e91f65704a0c3d5761b7f4ba53e8eacf8e"}