{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:RBP6BQ5FHZFL266HD6P6MBVTOE","short_pith_number":"pith:RBP6BQ5F","canonical_record":{"source":{"id":"math-ph/0611076","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-11-27T17:12:07Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"c11a9ce5322dea1f6006a07dfd1b8fddf9fbf0391ff3ec617630dd8ef2e2ba39","abstract_canon_sha256":"8e37a1f29066800d1ee8980e154c68c971e5b7a9df900b02584431ead2747437"},"schema_version":"1.0"},"canonical_sha256":"885fe0c3a53e4abd7bc71f9fe606b371071a444cf0fb5cb2152353284cff22c2","source":{"kind":"arxiv","id":"math-ph/0611076","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0611076","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0611076v1","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0611076","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"RBP6BQ5FHZFL","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"RBP6BQ5FHZFL266H","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"RBP6BQ5F","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:RBP6BQ5FHZFL266HD6P6MBVTOE","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0611076","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-11-27T17:12:07Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"c11a9ce5322dea1f6006a07dfd1b8fddf9fbf0391ff3ec617630dd8ef2e2ba39","abstract_canon_sha256":"8e37a1f29066800d1ee8980e154c68c971e5b7a9df900b02584431ead2747437"},"schema_version":"1.0"},"canonical_sha256":"885fe0c3a53e4abd7bc71f9fe606b371071a444cf0fb5cb2152353284cff22c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:59.735758Z","signature_b64":"D87yLFMjO1TTQfvV1oH+ry8XdKjRl+MZWw9hYqBJItAyGrJ1hW+pwIIpk3+pnb9kCil/MIiksCKg0Kt7mdPPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"885fe0c3a53e4abd7bc71f9fe606b371071a444cf0fb5cb2152353284cff22c2","last_reissued_at":"2026-05-18T01:20:59.735205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:59.735205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0611076","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":"2026-05-18T01:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zLgRiNm0PyaJVTJkDgUutRLFYBcWccMxVI/1ZdGO7h1K5UatcW6nERMqQwQHs7r9vosTOE6wIhZvRNe7hokxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:37:13.435828Z"},"content_sha256":"2d8eb349e1207b95ed950612348d33e8d1509876aeaea9d6c59d16d987680626","schema_version":"1.0","event_id":"sha256:2d8eb349e1207b95ed950612348d33e8d1509876aeaea9d6c59d16d987680626"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:RBP6BQ5FHZFL266HD6P6MBVTOE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Soft and hard wall in a stochastic reaction diffusion equation","license":"","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"L. Bertini, P. Butt\\`a, S. Brassesco","submitted_at":"2006-11-27T17:12:07Z","abstract_excerpt":"We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two stable phases, as the intensity of the noise vanishes and the size of the interval diverges. In particular, we prove that, in a suitable scaling limit, the front evolves according to a one-dimensional diffusion process with a non-linear drift accounting for a \"soft\" repulsion from the boundary. We finally show how a \"hard\" repulsion can be obtained by an extra di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0611076","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":"2026-05-18T01:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rD8GFoY1gCPzcPCI/BFVxT3Ss3Yyh4UeNJnofs2VaQiPW6sinR1JJXZS4EgXQ0Pbarq6jJkTfewoZNB8tAqiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:37:13.436182Z"},"content_sha256":"9417ee5b7ae2fc98a35afa20765710fac924ce1f559eb7498386e1520cd535ce","schema_version":"1.0","event_id":"sha256:9417ee5b7ae2fc98a35afa20765710fac924ce1f559eb7498386e1520cd535ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBP6BQ5FHZFL266HD6P6MBVTOE/bundle.json","state_url":"https://pith.science/pith/RBP6BQ5FHZFL266HD6P6MBVTOE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBP6BQ5FHZFL266HD6P6MBVTOE/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":"2026-06-28T15:37:13Z","links":{"resolver":"https://pith.science/pith/RBP6BQ5FHZFL266HD6P6MBVTOE","bundle":"https://pith.science/pith/RBP6BQ5FHZFL266HD6P6MBVTOE/bundle.json","state":"https://pith.science/pith/RBP6BQ5FHZFL266HD6P6MBVTOE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBP6BQ5FHZFL266HD6P6MBVTOE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:RBP6BQ5FHZFL266HD6P6MBVTOE","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":"8e37a1f29066800d1ee8980e154c68c971e5b7a9df900b02584431ead2747437","cross_cats_sorted":["math.MP","math.PR"],"license":"","primary_cat":"math-ph","submitted_at":"2006-11-27T17:12:07Z","title_canon_sha256":"c11a9ce5322dea1f6006a07dfd1b8fddf9fbf0391ff3ec617630dd8ef2e2ba39"},"schema_version":"1.0","source":{"id":"math-ph/0611076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0611076","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0611076v1","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0611076","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"RBP6BQ5FHZFL","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"RBP6BQ5FHZFL266H","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"RBP6BQ5F","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:9417ee5b7ae2fc98a35afa20765710fac924ce1f559eb7498386e1520cd535ce","target":"graph","created_at":"2026-05-18T01:20:59Z","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 stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two stable phases, as the intensity of the noise vanishes and the size of the interval diverges. In particular, we prove that, in a suitable scaling limit, the front evolves according to a one-dimensional diffusion process with a non-linear drift accounting for a \"soft\" repulsion from the boundary. We finally show how a \"hard\" repulsion can be obtained by an extra di","authors_text":"L. Bertini, P. Butt\\`a, S. Brassesco","cross_cats":["math.MP","math.PR"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-11-27T17:12:07Z","title":"Soft and hard wall in a stochastic reaction diffusion equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0611076","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":"sha256:2d8eb349e1207b95ed950612348d33e8d1509876aeaea9d6c59d16d987680626","target":"record","created_at":"2026-05-18T01:20:59Z","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":"8e37a1f29066800d1ee8980e154c68c971e5b7a9df900b02584431ead2747437","cross_cats_sorted":["math.MP","math.PR"],"license":"","primary_cat":"math-ph","submitted_at":"2006-11-27T17:12:07Z","title_canon_sha256":"c11a9ce5322dea1f6006a07dfd1b8fddf9fbf0391ff3ec617630dd8ef2e2ba39"},"schema_version":"1.0","source":{"id":"math-ph/0611076","kind":"arxiv","version":1}},"canonical_sha256":"885fe0c3a53e4abd7bc71f9fe606b371071a444cf0fb5cb2152353284cff22c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"885fe0c3a53e4abd7bc71f9fe606b371071a444cf0fb5cb2152353284cff22c2","first_computed_at":"2026-05-18T01:20:59.735205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:59.735205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D87yLFMjO1TTQfvV1oH+ry8XdKjRl+MZWw9hYqBJItAyGrJ1hW+pwIIpk3+pnb9kCil/MIiksCKg0Kt7mdPPBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:59.735758Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0611076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d8eb349e1207b95ed950612348d33e8d1509876aeaea9d6c59d16d987680626","sha256:9417ee5b7ae2fc98a35afa20765710fac924ce1f559eb7498386e1520cd535ce"],"state_sha256":"712333f23732fbd6eeca20253135d37117ce4519b7be5d2c55596d4fed3f40cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XCElFOMRYfStvL++jb0MPmD6nyKdqddvfgpyOA4NKvQe+cfpzAh9/JjAaH5rJMtQK+LBWe6g4WTTI8OxW/X1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T15:37:13.438852Z","bundle_sha256":"1c794e65f9d1dfbbc57b75eee8e4a948b0f7695e714cc4b0b751fed9fe59692a"}}