{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:ZHTY6ZF5NRUFM5HDXG3RX55JTT","short_pith_number":"pith:ZHTY6ZF5","canonical_record":{"source":{"id":"0805.1708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-05-12T18:41:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a05660fcaaf35315cef8c89569d7d3d99600834e8f8030a90e80657c72f8f877","abstract_canon_sha256":"af0664aa496283737d8f4664e05a5860f11ed1bb9695209069cff86c37ff2115"},"schema_version":"1.0"},"canonical_sha256":"c9e78f64bd6c685674e3b9b71bf7a99cec7fc26e4d9525b581c72b5a910540ec","source":{"kind":"arxiv","id":"0805.1708","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.1708","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"arxiv_version","alias_value":"0805.1708v1","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.1708","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZHTY6ZF5NRUF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZHTY6ZF5NRUFM5HD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZHTY6ZF5","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:ZHTY6ZF5NRUFM5HDXG3RX55JTT","target":"record","payload":{"canonical_record":{"source":{"id":"0805.1708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-05-12T18:41:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a05660fcaaf35315cef8c89569d7d3d99600834e8f8030a90e80657c72f8f877","abstract_canon_sha256":"af0664aa496283737d8f4664e05a5860f11ed1bb9695209069cff86c37ff2115"},"schema_version":"1.0"},"canonical_sha256":"c9e78f64bd6c685674e3b9b71bf7a99cec7fc26e4d9525b581c72b5a910540ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:52.832389Z","signature_b64":"upFoy1BK3r2AGtFfGVh52o7oKUxMZyvWDUIlZdff+puhR4EXxt1IEJVKlmQ9KBsToOsIY0LLvk9O1Xyzaed8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9e78f64bd6c685674e3b9b71bf7a99cec7fc26e4d9525b581c72b5a910540ec","last_reissued_at":"2026-05-18T02:15:52.831766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:52.831766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0805.1708","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:15:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQhcwSg4WdMKJqrJ8Yz5egCYeOy7Aldnm7t2d7ZUbl9rel/Oa0krfcdDmLDvmt/ac6eOG3ufxmvAHabNAbRVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:03:04.815659Z"},"content_sha256":"dae193eec6acbe90c5b669fd168b201dece46e2b107079c972a6aaa0c055c51a","schema_version":"1.0","event_id":"sha256:dae193eec6acbe90c5b669fd168b201dece46e2b107079c972a6aaa0c055c51a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:ZHTY6ZF5NRUFM5HDXG3RX55JTT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quenched and Annealed Critical Points in Polymer Pinning Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Kenneth S. Alexander, Nikos Zygouras","submitted_at":"2008-05-12T18:41:56Z","abstract_excerpt":"We consider a polymer with configuration modeled by the path of a Markov chain, interacting with a potential $u+V_n$ which the chain encounters when it visits a special state 0 at time $n$. The disorder $(V_n)$ is a fixed realization of an i.i.d. sequence. The polymer is pinned, i.e. the chain spends a positive fraction of its time at state 0, when $u$ exceeds a critical value. We assume that for the Markov chain in the absence of the potential, the probability of an excursion from 0 of length $n$ has the form $n^{-c}\\phi(n)$ with $c \\geq 1$ and $\\phi$ slowly varying. Comparing to the correspo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1708","kind":"arxiv","version":1},"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":"2026-05-18T02:15:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6JXF7Z06b1SOA6tTSB5DqFAPIRtCr5HUPFpEBzjyVDNHDVk0RfsX7lDkYcpcbVIV5nroVDBEhOxRs2OduP1NBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:03:04.816100Z"},"content_sha256":"9accb882390dcab0b9c170884c344ac6315ad018b78ad8cba9ac9c97f102dc5b","schema_version":"1.0","event_id":"sha256:9accb882390dcab0b9c170884c344ac6315ad018b78ad8cba9ac9c97f102dc5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZHTY6ZF5NRUFM5HDXG3RX55JTT/bundle.json","state_url":"https://pith.science/pith/ZHTY6ZF5NRUFM5HDXG3RX55JTT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZHTY6ZF5NRUFM5HDXG3RX55JTT/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":"2026-05-31T11:03:04Z","links":{"resolver":"https://pith.science/pith/ZHTY6ZF5NRUFM5HDXG3RX55JTT","bundle":"https://pith.science/pith/ZHTY6ZF5NRUFM5HDXG3RX55JTT/bundle.json","state":"https://pith.science/pith/ZHTY6ZF5NRUFM5HDXG3RX55JTT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZHTY6ZF5NRUFM5HDXG3RX55JTT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:ZHTY6ZF5NRUFM5HDXG3RX55JTT","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":"af0664aa496283737d8f4664e05a5860f11ed1bb9695209069cff86c37ff2115","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-05-12T18:41:56Z","title_canon_sha256":"a05660fcaaf35315cef8c89569d7d3d99600834e8f8030a90e80657c72f8f877"},"schema_version":"1.0","source":{"id":"0805.1708","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.1708","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"arxiv_version","alias_value":"0805.1708v1","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.1708","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZHTY6ZF5NRUF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZHTY6ZF5NRUFM5HD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZHTY6ZF5","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:9accb882390dcab0b9c170884c344ac6315ad018b78ad8cba9ac9c97f102dc5b","target":"graph","created_at":"2026-05-18T02:15:52Z","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 polymer with configuration modeled by the path of a Markov chain, interacting with a potential $u+V_n$ which the chain encounters when it visits a special state 0 at time $n$. The disorder $(V_n)$ is a fixed realization of an i.i.d. sequence. The polymer is pinned, i.e. the chain spends a positive fraction of its time at state 0, when $u$ exceeds a critical value. We assume that for the Markov chain in the absence of the potential, the probability of an excursion from 0 of length $n$ has the form $n^{-c}\\phi(n)$ with $c \\geq 1$ and $\\phi$ slowly varying. Comparing to the correspo","authors_text":"Kenneth S. Alexander, Nikos Zygouras","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-05-12T18:41:56Z","title":"Quenched and Annealed Critical Points in Polymer Pinning Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1708","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:dae193eec6acbe90c5b669fd168b201dece46e2b107079c972a6aaa0c055c51a","target":"record","created_at":"2026-05-18T02:15:52Z","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":"af0664aa496283737d8f4664e05a5860f11ed1bb9695209069cff86c37ff2115","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-05-12T18:41:56Z","title_canon_sha256":"a05660fcaaf35315cef8c89569d7d3d99600834e8f8030a90e80657c72f8f877"},"schema_version":"1.0","source":{"id":"0805.1708","kind":"arxiv","version":1}},"canonical_sha256":"c9e78f64bd6c685674e3b9b71bf7a99cec7fc26e4d9525b581c72b5a910540ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9e78f64bd6c685674e3b9b71bf7a99cec7fc26e4d9525b581c72b5a910540ec","first_computed_at":"2026-05-18T02:15:52.831766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:52.831766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"upFoy1BK3r2AGtFfGVh52o7oKUxMZyvWDUIlZdff+puhR4EXxt1IEJVKlmQ9KBsToOsIY0LLvk9O1Xyzaed8Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:52.832389Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.1708","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dae193eec6acbe90c5b669fd168b201dece46e2b107079c972a6aaa0c055c51a","sha256:9accb882390dcab0b9c170884c344ac6315ad018b78ad8cba9ac9c97f102dc5b"],"state_sha256":"1cd2b4832396247bfc2221854a4f2dbfef47ec05d06af0c21b095e01175fc4ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ByuTYiuf7VHhbcErM6V+e4ZLRodUd6+zidopZm8dvvh+wSA7cjZOkbc7/uuCv5OxMU83q9QDJTDqUe+gwLOpDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:03:04.820144Z","bundle_sha256":"d53e90016779676929d49f615853e43a4f654e6cee0b6eedbe8820f9e2fcf47f"}}