{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OZDJXGZHNVCAUIMNF3TIAVWD2B","short_pith_number":"pith:OZDJXGZH","canonical_record":{"source":{"id":"1203.3038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-14T10:30:22Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"99defbad255a4d158be4468e3330448f66a4a8a1a27d1bab32249d0b937815b2","abstract_canon_sha256":"2e8cc91a1383f79793b311ca861ce06cd035ac83ae245711ce681bcdf19c3b90"},"schema_version":"1.0"},"canonical_sha256":"76469b9b276d440a218d2ee68056c3d0596b5525ddec2064a1d88c6f41c1e79a","source":{"kind":"arxiv","id":"1203.3038","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3038","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3038v2","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3038","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"pith_short_12","alias_value":"OZDJXGZHNVCA","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"OZDJXGZHNVCAUIMN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"OZDJXGZH","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OZDJXGZHNVCAUIMNF3TIAVWD2B","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-14T10:30:22Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"99defbad255a4d158be4468e3330448f66a4a8a1a27d1bab32249d0b937815b2","abstract_canon_sha256":"2e8cc91a1383f79793b311ca861ce06cd035ac83ae245711ce681bcdf19c3b90"},"schema_version":"1.0"},"canonical_sha256":"76469b9b276d440a218d2ee68056c3d0596b5525ddec2064a1d88c6f41c1e79a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:58.063049Z","signature_b64":"GdPpr8waNa52VuYzFPT6BYvPWxfJH0yhjofF1ZoDWqaM23vCrRngtie6gyFlW2x1NVgkWtu9Dk5wVBSwkbssAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76469b9b276d440a218d2ee68056c3d0596b5525ddec2064a1d88c6f41c1e79a","last_reissued_at":"2026-05-18T03:49:58.062297Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:58.062297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3038","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":"2026-05-18T03:49:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ihJOuR8my3ZxLxY5yLe/xtPHLpAZmfYKn8ReMnMlw4Rq1F508d7ipjxZUs3Kkh8nj2t2RzUbGWgjWGerqsEYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:48:37.810985Z"},"content_sha256":"1ad0547680042ac44d0f11193378d7d51c97f860ccb584debd2d11664c464911","schema_version":"1.0","event_id":"sha256:1ad0547680042ac44d0f11193378d7d51c97f860ccb584debd2d11664c464911"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OZDJXGZHNVCAUIMNF3TIAVWD2B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Corrections to Scaling for Watersheds, Optimal Path Cracks, and Bridge Lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"D. Kadau, E. Fehr, H. J. Herrmann, J. S. Andrade Jr, K. J. Schrenk, N. A. M. Ara\\'ujo, P. Grassberger","submitted_at":"2012-03-14T10:30:22Z","abstract_excerpt":"We study the corrections to scaling for the mass of the watershed, the bridge line, and the optimal path crack in two and three dimensions. We disclose that these models have numerically equivalent fractal dimensions and leading correction-to-scaling exponents. We conjecture all three models to possess the same fractal dimension, namely, $d_f=1.2168\\pm0.0005$ in 2D and $d_f=2.487\\pm0.003$ in 3D, and the same exponent of the leading correction, $\\Omega=0.9\\pm0.1$ and $\\Omega=1.0\\pm0.1$, respectively. The close relations between watersheds, optimal path cracks in the strong disorder limit, and b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3038","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":"2026-05-18T03:49:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPLD2EDVJnm9xc2owtJCAfzPuOV8FMx3AKm5zQMfyHILQoynh1ffu8xKijrcZ18KDmoq8Gw5Si1bd9UhbGsKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:48:37.811341Z"},"content_sha256":"ed2d9a08801880ea3bbedb408eaa3cfaa9cc316dea0d32534208e6ff11a23df6","schema_version":"1.0","event_id":"sha256:ed2d9a08801880ea3bbedb408eaa3cfaa9cc316dea0d32534208e6ff11a23df6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OZDJXGZHNVCAUIMNF3TIAVWD2B/bundle.json","state_url":"https://pith.science/pith/OZDJXGZHNVCAUIMNF3TIAVWD2B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OZDJXGZHNVCAUIMNF3TIAVWD2B/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":"2026-06-21T20:48:37Z","links":{"resolver":"https://pith.science/pith/OZDJXGZHNVCAUIMNF3TIAVWD2B","bundle":"https://pith.science/pith/OZDJXGZHNVCAUIMNF3TIAVWD2B/bundle.json","state":"https://pith.science/pith/OZDJXGZHNVCAUIMNF3TIAVWD2B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OZDJXGZHNVCAUIMNF3TIAVWD2B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OZDJXGZHNVCAUIMNF3TIAVWD2B","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":"2e8cc91a1383f79793b311ca861ce06cd035ac83ae245711ce681bcdf19c3b90","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-14T10:30:22Z","title_canon_sha256":"99defbad255a4d158be4468e3330448f66a4a8a1a27d1bab32249d0b937815b2"},"schema_version":"1.0","source":{"id":"1203.3038","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3038","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3038v2","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3038","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"pith_short_12","alias_value":"OZDJXGZHNVCA","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"OZDJXGZHNVCAUIMN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"OZDJXGZH","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:ed2d9a08801880ea3bbedb408eaa3cfaa9cc316dea0d32534208e6ff11a23df6","target":"graph","created_at":"2026-05-18T03:49:58Z","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 the corrections to scaling for the mass of the watershed, the bridge line, and the optimal path crack in two and three dimensions. We disclose that these models have numerically equivalent fractal dimensions and leading correction-to-scaling exponents. We conjecture all three models to possess the same fractal dimension, namely, $d_f=1.2168\\pm0.0005$ in 2D and $d_f=2.487\\pm0.003$ in 3D, and the same exponent of the leading correction, $\\Omega=0.9\\pm0.1$ and $\\Omega=1.0\\pm0.1$, respectively. The close relations between watersheds, optimal path cracks in the strong disorder limit, and b","authors_text":"D. Kadau, E. Fehr, H. J. Herrmann, J. S. Andrade Jr, K. J. Schrenk, N. A. M. Ara\\'ujo, P. Grassberger","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-14T10:30:22Z","title":"Corrections to Scaling for Watersheds, Optimal Path Cracks, and Bridge Lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3038","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":"sha256:1ad0547680042ac44d0f11193378d7d51c97f860ccb584debd2d11664c464911","target":"record","created_at":"2026-05-18T03:49:58Z","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":"2e8cc91a1383f79793b311ca861ce06cd035ac83ae245711ce681bcdf19c3b90","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-14T10:30:22Z","title_canon_sha256":"99defbad255a4d158be4468e3330448f66a4a8a1a27d1bab32249d0b937815b2"},"schema_version":"1.0","source":{"id":"1203.3038","kind":"arxiv","version":2}},"canonical_sha256":"76469b9b276d440a218d2ee68056c3d0596b5525ddec2064a1d88c6f41c1e79a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76469b9b276d440a218d2ee68056c3d0596b5525ddec2064a1d88c6f41c1e79a","first_computed_at":"2026-05-18T03:49:58.062297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:58.062297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GdPpr8waNa52VuYzFPT6BYvPWxfJH0yhjofF1ZoDWqaM23vCrRngtie6gyFlW2x1NVgkWtu9Dk5wVBSwkbssAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:58.063049Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3038","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ad0547680042ac44d0f11193378d7d51c97f860ccb584debd2d11664c464911","sha256:ed2d9a08801880ea3bbedb408eaa3cfaa9cc316dea0d32534208e6ff11a23df6"],"state_sha256":"21843f1b051a8e027fc9ddc8e4c15d152a108d29dfee4cc19ba738216a063658"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NrhdWp3otA9xo11LN+6RlNpX69ye5z6neRp0oW7LJaO+hCE090kGXPnfNl+efLCBN4NaP+02dQcGD02/FkyPAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:48:37.813308Z","bundle_sha256":"7b14cc013270f7f8fb2418ec2d4812509142c04beec9b3fcbdf2b3fd67afa72e"}}