{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:E6BTLDC7NSM63Y7LFENF3EKBIZ","short_pith_number":"pith:E6BTLDC7","canonical_record":{"source":{"id":"2409.08745","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-13T11:52:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"6c6432d6bc2182d8d30e211ac389b7818562aafeabb7bd3b05564c1dea0fc1cf","abstract_canon_sha256":"59e9ea38e04ef2bbcbb3277e20406e98db8813051a61ea0bc20159ac4c55bd0f"},"schema_version":"1.0"},"canonical_sha256":"2783358c5f6c99ede3eb291a5d91414665e7c8bd347f04a093ba152f6753943a","source":{"kind":"arxiv","id":"2409.08745","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.08745","created_at":"2026-07-05T09:06:46Z"},{"alias_kind":"arxiv_version","alias_value":"2409.08745v1","created_at":"2026-07-05T09:06:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.08745","created_at":"2026-07-05T09:06:46Z"},{"alias_kind":"pith_short_12","alias_value":"E6BTLDC7NSM6","created_at":"2026-07-05T09:06:46Z"},{"alias_kind":"pith_short_16","alias_value":"E6BTLDC7NSM63Y7L","created_at":"2026-07-05T09:06:46Z"},{"alias_kind":"pith_short_8","alias_value":"E6BTLDC7","created_at":"2026-07-05T09:06:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:E6BTLDC7NSM63Y7LFENF3EKBIZ","target":"record","payload":{"canonical_record":{"source":{"id":"2409.08745","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-13T11:52:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"6c6432d6bc2182d8d30e211ac389b7818562aafeabb7bd3b05564c1dea0fc1cf","abstract_canon_sha256":"59e9ea38e04ef2bbcbb3277e20406e98db8813051a61ea0bc20159ac4c55bd0f"},"schema_version":"1.0"},"canonical_sha256":"2783358c5f6c99ede3eb291a5d91414665e7c8bd347f04a093ba152f6753943a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:06:46.647019Z","signature_b64":"WqxqJRmMZSkutPRxECCwi70zdwqKiH0XqboWRHoRu7g220TMJazZcRZw44M4dgqIGLXgOv5W6W8T+sJvF8nQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2783358c5f6c99ede3eb291a5d91414665e7c8bd347f04a093ba152f6753943a","last_reissued_at":"2026-07-05T09:06:46.646536Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:06:46.646536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.08745","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":"2026-07-05T09:06:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0TWYatzN14G6D2MAhAu4CcZufcr/wNJdGMUtuC5CS0eicgFYUwaFEYEREnCAizFqkn+WpwhwLe8FkWh3M5OCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:41:13.544431Z"},"content_sha256":"112d37bdd254d6a4c9d33bb72e3bf0b964c38ee0ea34be90dca81c4daa41d552","schema_version":"1.0","event_id":"sha256:112d37bdd254d6a4c9d33bb72e3bf0b964c38ee0ea34be90dca81c4daa41d552"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:E6BTLDC7NSM63Y7LFENF3EKBIZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tilted Solid-On-Solid is liquid: scaling limit of SOS with a potential on a slope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Beno\\^it Laslier, Eyal Lubetzky","submitted_at":"2024-09-13T11:52:17Z","abstract_excerpt":"The $(2+1)$D Solid-On-Solid (SOS) model famously exhibits a roughening transition: on an $N\\times N$ torus with the height at the origin rooted at $0$, the variance of $h(x)$, the height at $x$, is $O(1)$ at large inverse-temperature $\\beta$, vs. $\\asymp \\log |x|$ at small $\\beta$ (as in the Gaussian free field (GFF)). The former--rigidity at large $\\beta$--is known for a wide class of $|\\nabla\\phi|^p$ models ($p=1$ being SOS) yet is believed to fail once the surface is on a slope (tilted boundary conditions). It is conjectured that the slope would destabilize the rigidity and induce the GFF-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.08745","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.08745/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:06:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0elVFoKYwHFBCDBC04SciTczFekj6lByBc7YPnM1s95dqf4DVAJ82vmOZhX+vmVfc/zq9pEolrswJaA4kmQnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:41:13.544947Z"},"content_sha256":"2aa42be20009ee9bb33fbd4da1a70bda035ac1b5ce836c6288d3c846c096e1e0","schema_version":"1.0","event_id":"sha256:2aa42be20009ee9bb33fbd4da1a70bda035ac1b5ce836c6288d3c846c096e1e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E6BTLDC7NSM63Y7LFENF3EKBIZ/bundle.json","state_url":"https://pith.science/pith/E6BTLDC7NSM63Y7LFENF3EKBIZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E6BTLDC7NSM63Y7LFENF3EKBIZ/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":"2026-08-08T19:41:13Z","links":{"resolver":"https://pith.science/pith/E6BTLDC7NSM63Y7LFENF3EKBIZ","bundle":"https://pith.science/pith/E6BTLDC7NSM63Y7LFENF3EKBIZ/bundle.json","state":"https://pith.science/pith/E6BTLDC7NSM63Y7LFENF3EKBIZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E6BTLDC7NSM63Y7LFENF3EKBIZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:E6BTLDC7NSM63Y7LFENF3EKBIZ","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":"59e9ea38e04ef2bbcbb3277e20406e98db8813051a61ea0bc20159ac4c55bd0f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-13T11:52:17Z","title_canon_sha256":"6c6432d6bc2182d8d30e211ac389b7818562aafeabb7bd3b05564c1dea0fc1cf"},"schema_version":"1.0","source":{"id":"2409.08745","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.08745","created_at":"2026-07-05T09:06:46Z"},{"alias_kind":"arxiv_version","alias_value":"2409.08745v1","created_at":"2026-07-05T09:06:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.08745","created_at":"2026-07-05T09:06:46Z"},{"alias_kind":"pith_short_12","alias_value":"E6BTLDC7NSM6","created_at":"2026-07-05T09:06:46Z"},{"alias_kind":"pith_short_16","alias_value":"E6BTLDC7NSM63Y7L","created_at":"2026-07-05T09:06:46Z"},{"alias_kind":"pith_short_8","alias_value":"E6BTLDC7","created_at":"2026-07-05T09:06:46Z"}],"graph_snapshots":[{"event_id":"sha256:2aa42be20009ee9bb33fbd4da1a70bda035ac1b5ce836c6288d3c846c096e1e0","target":"graph","created_at":"2026-07-05T09:06:46Z","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/2409.08745/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $(2+1)$D Solid-On-Solid (SOS) model famously exhibits a roughening transition: on an $N\\times N$ torus with the height at the origin rooted at $0$, the variance of $h(x)$, the height at $x$, is $O(1)$ at large inverse-temperature $\\beta$, vs. $\\asymp \\log |x|$ at small $\\beta$ (as in the Gaussian free field (GFF)). The former--rigidity at large $\\beta$--is known for a wide class of $|\\nabla\\phi|^p$ models ($p=1$ being SOS) yet is believed to fail once the surface is on a slope (tilted boundary conditions). It is conjectured that the slope would destabilize the rigidity and induce the GFF-t","authors_text":"Beno\\^it Laslier, Eyal Lubetzky","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-13T11:52:17Z","title":"Tilted Solid-On-Solid is liquid: scaling limit of SOS with a potential on a slope"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.08745","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":"sha256:112d37bdd254d6a4c9d33bb72e3bf0b964c38ee0ea34be90dca81c4daa41d552","target":"record","created_at":"2026-07-05T09:06:46Z","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":"59e9ea38e04ef2bbcbb3277e20406e98db8813051a61ea0bc20159ac4c55bd0f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-13T11:52:17Z","title_canon_sha256":"6c6432d6bc2182d8d30e211ac389b7818562aafeabb7bd3b05564c1dea0fc1cf"},"schema_version":"1.0","source":{"id":"2409.08745","kind":"arxiv","version":1}},"canonical_sha256":"2783358c5f6c99ede3eb291a5d91414665e7c8bd347f04a093ba152f6753943a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2783358c5f6c99ede3eb291a5d91414665e7c8bd347f04a093ba152f6753943a","first_computed_at":"2026-07-05T09:06:46.646536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:06:46.646536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WqxqJRmMZSkutPRxECCwi70zdwqKiH0XqboWRHoRu7g220TMJazZcRZw44M4dgqIGLXgOv5W6W8T+sJvF8nQCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:06:46.647019Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.08745","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:112d37bdd254d6a4c9d33bb72e3bf0b964c38ee0ea34be90dca81c4daa41d552","sha256:2aa42be20009ee9bb33fbd4da1a70bda035ac1b5ce836c6288d3c846c096e1e0"],"state_sha256":"78598c699d0af738b8a948d3e656d91e681292204fb083748fa54f53d6d6ada8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WcYjhc6KM/KM39KByfiNqV86Gf70tI4v0tbC/wcMn36sf6Uc3thjvCLL7bAlM9a0+3GwpeuTnLAMAHqIscxmCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T19:41:13.551704Z","bundle_sha256":"642f417b074f55b022313c8d1af27b23e2d2cdcfcd9a8c64481414da1ebe7ed2"}}