{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UXBITDJS66GM7CUWKAAQ5QKQR2","short_pith_number":"pith:UXBITDJS","canonical_record":{"source":{"id":"1206.1231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-06T14:05:30Z","cross_cats_sorted":[],"title_canon_sha256":"514ffb6cd857ac1d0aacbaaff2e7e9a45c34a671bf0b4babd5c9e50870b2c647","abstract_canon_sha256":"efe5b93a07f3a819aae36c637dbc01d25e8b17e1017f7fdc6c75a4196b54e820"},"schema_version":"1.0"},"canonical_sha256":"a5c2898d32f78ccf8a9650010ec1508e86fb713096dea01a9da6011006e40b33","source":{"kind":"arxiv","id":"1206.1231","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1231","created_at":"2026-05-18T01:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1231v2","created_at":"2026-05-18T01:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1231","created_at":"2026-05-18T01:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"UXBITDJS66GM","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UXBITDJS66GM7CUW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UXBITDJS","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UXBITDJS66GM7CUWKAAQ5QKQR2","target":"record","payload":{"canonical_record":{"source":{"id":"1206.1231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-06T14:05:30Z","cross_cats_sorted":[],"title_canon_sha256":"514ffb6cd857ac1d0aacbaaff2e7e9a45c34a671bf0b4babd5c9e50870b2c647","abstract_canon_sha256":"efe5b93a07f3a819aae36c637dbc01d25e8b17e1017f7fdc6c75a4196b54e820"},"schema_version":"1.0"},"canonical_sha256":"a5c2898d32f78ccf8a9650010ec1508e86fb713096dea01a9da6011006e40b33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:10.725057Z","signature_b64":"8R9Y7hQJY6HNAQ2sqQ4fZLn34GwTt5yM8WBOcoiycfcLawFLG4eaKRYYcLLPa2N4GwRXBpOhCVAB9YBViavnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5c2898d32f78ccf8a9650010ec1508e86fb713096dea01a9da6011006e40b33","last_reissued_at":"2026-05-18T01:22:10.724436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:10.724436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.1231","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CWo/jN4298a0+6dSNXkfTryQlOqrkBJBitiyQIxqJdQuBpJ5eVJS7yzRmsLdhEC9EOcpnM8kzmCIBbzxDpOdCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:33:53.236401Z"},"content_sha256":"a7ded9da22e8ea3993247d4e623bbd3b2c16915ef04344a128b1caff133566e2","schema_version":"1.0","event_id":"sha256:a7ded9da22e8ea3993247d4e623bbd3b2c16915ef04344a128b1caff133566e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UXBITDJS66GM7CUWKAAQ5QKQR2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localization Transition for Polymers in Poissonian Medium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Francis Comets, Nobuo Yoshida","submitted_at":"2012-06-06T14:05:30Z","abstract_excerpt":"We study a model of directed polymers in random environment in dimension $1+d$, given by a Brownian motion in a Poissonian potential. We study the effect of the density and the strength of inhomogeneities, respectively the intensity parameter $\\nu$ of the Poisson field and the temperature inverse $\\beta$. Our results are: (i) fine information on the phase diagram, with quantitative estimates on the critical curve; (ii) pathwise localization at low temperature and/or large density; (iii) complete localization in a favourite corridor for large $\\nu \\beta^2$ and bounded $\\beta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1231","kind":"arxiv","version":2},"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":"2026-05-18T01:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k+84YjpNkYBqahGrPcsl/QfmaCk3w89X5DRwNAKEO5DWlSRXTho3MY3dTSt6M9wvueLFXJwC5b07IgGzw1HsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:33:53.236769Z"},"content_sha256":"dbf203ffe78662d9cda9a6ba49608f6f521876d9226e1635a46352162badc933","schema_version":"1.0","event_id":"sha256:dbf203ffe78662d9cda9a6ba49608f6f521876d9226e1635a46352162badc933"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXBITDJS66GM7CUWKAAQ5QKQR2/bundle.json","state_url":"https://pith.science/pith/UXBITDJS66GM7CUWKAAQ5QKQR2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXBITDJS66GM7CUWKAAQ5QKQR2/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":"2026-06-27T05:33:53Z","links":{"resolver":"https://pith.science/pith/UXBITDJS66GM7CUWKAAQ5QKQR2","bundle":"https://pith.science/pith/UXBITDJS66GM7CUWKAAQ5QKQR2/bundle.json","state":"https://pith.science/pith/UXBITDJS66GM7CUWKAAQ5QKQR2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXBITDJS66GM7CUWKAAQ5QKQR2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UXBITDJS66GM7CUWKAAQ5QKQR2","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":"efe5b93a07f3a819aae36c637dbc01d25e8b17e1017f7fdc6c75a4196b54e820","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-06T14:05:30Z","title_canon_sha256":"514ffb6cd857ac1d0aacbaaff2e7e9a45c34a671bf0b4babd5c9e50870b2c647"},"schema_version":"1.0","source":{"id":"1206.1231","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1231","created_at":"2026-05-18T01:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1231v2","created_at":"2026-05-18T01:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1231","created_at":"2026-05-18T01:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"UXBITDJS66GM","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UXBITDJS66GM7CUW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UXBITDJS","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:dbf203ffe78662d9cda9a6ba49608f6f521876d9226e1635a46352162badc933","target":"graph","created_at":"2026-05-18T01:22:10Z","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 a model of directed polymers in random environment in dimension $1+d$, given by a Brownian motion in a Poissonian potential. We study the effect of the density and the strength of inhomogeneities, respectively the intensity parameter $\\nu$ of the Poisson field and the temperature inverse $\\beta$. Our results are: (i) fine information on the phase diagram, with quantitative estimates on the critical curve; (ii) pathwise localization at low temperature and/or large density; (iii) complete localization in a favourite corridor for large $\\nu \\beta^2$ and bounded $\\beta$.","authors_text":"Francis Comets, Nobuo Yoshida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-06T14:05:30Z","title":"Localization Transition for Polymers in Poissonian Medium"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1231","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:a7ded9da22e8ea3993247d4e623bbd3b2c16915ef04344a128b1caff133566e2","target":"record","created_at":"2026-05-18T01:22:10Z","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":"efe5b93a07f3a819aae36c637dbc01d25e8b17e1017f7fdc6c75a4196b54e820","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-06T14:05:30Z","title_canon_sha256":"514ffb6cd857ac1d0aacbaaff2e7e9a45c34a671bf0b4babd5c9e50870b2c647"},"schema_version":"1.0","source":{"id":"1206.1231","kind":"arxiv","version":2}},"canonical_sha256":"a5c2898d32f78ccf8a9650010ec1508e86fb713096dea01a9da6011006e40b33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5c2898d32f78ccf8a9650010ec1508e86fb713096dea01a9da6011006e40b33","first_computed_at":"2026-05-18T01:22:10.724436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:10.724436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8R9Y7hQJY6HNAQ2sqQ4fZLn34GwTt5yM8WBOcoiycfcLawFLG4eaKRYYcLLPa2N4GwRXBpOhCVAB9YBViavnCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:10.725057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.1231","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7ded9da22e8ea3993247d4e623bbd3b2c16915ef04344a128b1caff133566e2","sha256:dbf203ffe78662d9cda9a6ba49608f6f521876d9226e1635a46352162badc933"],"state_sha256":"0e6f56dda8693e0b0deecb768e48ba659708a676229946c500b58535e1b970d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQSH2VE1mna5eXdy23Y2xfeRGT+fnXHsC1lg43ZT0kCUGPYelkQPjkIhkOsRd1Sinn4xM16hOFL/cNXNB9+tCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T05:33:53.238455Z","bundle_sha256":"11118227630fbcb29c7e757432cc241ba08d79334236b489669e24ead28b0f83"}}