{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7KYYTNR267EHPP2M65NGAON53E","short_pith_number":"pith:7KYYTNR2","canonical_record":{"source":{"id":"1501.01326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-06T22:08:58Z","cross_cats_sorted":[],"title_canon_sha256":"ae3f98991214baabb8357ba5052d1eb91b0f8c4af9f1c0df85e4ec526e784370","abstract_canon_sha256":"14f2d1f640de31d4e19efc9b3864dc7ff8f6484517862e34a327bb85d26b5892"},"schema_version":"1.0"},"canonical_sha256":"fab189b63af7c877bf4cf75a6039bdd921c5f23596b25ef13a05a675b83745fe","source":{"kind":"arxiv","id":"1501.01326","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01326","created_at":"2026-05-18T02:29:54Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01326v1","created_at":"2026-05-18T02:29:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01326","created_at":"2026-05-18T02:29:54Z"},{"alias_kind":"pith_short_12","alias_value":"7KYYTNR267EH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7KYYTNR267EHPP2M","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7KYYTNR2","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7KYYTNR267EHPP2M65NGAON53E","target":"record","payload":{"canonical_record":{"source":{"id":"1501.01326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-06T22:08:58Z","cross_cats_sorted":[],"title_canon_sha256":"ae3f98991214baabb8357ba5052d1eb91b0f8c4af9f1c0df85e4ec526e784370","abstract_canon_sha256":"14f2d1f640de31d4e19efc9b3864dc7ff8f6484517862e34a327bb85d26b5892"},"schema_version":"1.0"},"canonical_sha256":"fab189b63af7c877bf4cf75a6039bdd921c5f23596b25ef13a05a675b83745fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:54.525016Z","signature_b64":"HZ0vZtitcomEMjtsI89chtvRU/RiVwJbQd7xVox16TGd+DDotrvvQYZn8DCkwn4AbqtpEjkUaX6ABk/6P6LyDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fab189b63af7c877bf4cf75a6039bdd921c5f23596b25ef13a05a675b83745fe","last_reissued_at":"2026-05-18T02:29:54.524603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:54.524603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.01326","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":"2026-05-18T02:29:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JgMuQDoHIxD7oUNyyiiEvFdVIEODUXPiA7R4zy++5Bb6BvXVbNnuLhU7zNf36uGOrFBP6mgqYT7hvSX7NXUkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:54:09.424448Z"},"content_sha256":"71154be14ba0e8e65bfebe336a14c6f6da8dd96809fa4d0d59d333c2c2662584","schema_version":"1.0","event_id":"sha256:71154be14ba0e8e65bfebe336a14c6f6da8dd96809fa4d0d59d333c2c2662584"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7KYYTNR267EHPP2M65NGAON53E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Front blocking and propagation in cylinders with varying cross section","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guillemette Chapuisat, Henri Berestycki, Juliette Bouhours","submitted_at":"2015-01-06T22:08:58Z","abstract_excerpt":"In this paper we consider a bistable reaction-diffusion equation in unbounded domains and we investigate the existence of propagation phenomena, possibly partial, in some direction or, on the contrary, of blocking phenomena. We start by proving the well-posedness of the problem. Then we prove that when the domain has a decreasing cross section with respect to the direction of propagation there is complete propagation. Further, we prove that the wave can be blocked as it comes to an abrupt geometry change. Finally we discuss various general geometrical properties that ensure either partial or c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01326","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":"2026-05-18T02:29:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bslzjr0NvVsKBev1tBARmw8ZitLq3uA/KWsLMrjaYZ5fISJGZUPeyd7thrHNeBsdtPLRAeI1E/J03AofcieMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:54:09.425153Z"},"content_sha256":"e6bf97a4a80e7f8be12990ccfcd6dd8d8fe92a407f4878f07de21f2c18af8d69","schema_version":"1.0","event_id":"sha256:e6bf97a4a80e7f8be12990ccfcd6dd8d8fe92a407f4878f07de21f2c18af8d69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7KYYTNR267EHPP2M65NGAON53E/bundle.json","state_url":"https://pith.science/pith/7KYYTNR267EHPP2M65NGAON53E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7KYYTNR267EHPP2M65NGAON53E/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":"2026-05-26T21:54:09Z","links":{"resolver":"https://pith.science/pith/7KYYTNR267EHPP2M65NGAON53E","bundle":"https://pith.science/pith/7KYYTNR267EHPP2M65NGAON53E/bundle.json","state":"https://pith.science/pith/7KYYTNR267EHPP2M65NGAON53E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7KYYTNR267EHPP2M65NGAON53E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7KYYTNR267EHPP2M65NGAON53E","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":"14f2d1f640de31d4e19efc9b3864dc7ff8f6484517862e34a327bb85d26b5892","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-06T22:08:58Z","title_canon_sha256":"ae3f98991214baabb8357ba5052d1eb91b0f8c4af9f1c0df85e4ec526e784370"},"schema_version":"1.0","source":{"id":"1501.01326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01326","created_at":"2026-05-18T02:29:54Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01326v1","created_at":"2026-05-18T02:29:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01326","created_at":"2026-05-18T02:29:54Z"},{"alias_kind":"pith_short_12","alias_value":"7KYYTNR267EH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7KYYTNR267EHPP2M","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7KYYTNR2","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:e6bf97a4a80e7f8be12990ccfcd6dd8d8fe92a407f4878f07de21f2c18af8d69","target":"graph","created_at":"2026-05-18T02:29:54Z","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":"In this paper we consider a bistable reaction-diffusion equation in unbounded domains and we investigate the existence of propagation phenomena, possibly partial, in some direction or, on the contrary, of blocking phenomena. We start by proving the well-posedness of the problem. Then we prove that when the domain has a decreasing cross section with respect to the direction of propagation there is complete propagation. Further, we prove that the wave can be blocked as it comes to an abrupt geometry change. Finally we discuss various general geometrical properties that ensure either partial or c","authors_text":"Guillemette Chapuisat, Henri Berestycki, Juliette Bouhours","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-06T22:08:58Z","title":"Front blocking and propagation in cylinders with varying cross section"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01326","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":"sha256:71154be14ba0e8e65bfebe336a14c6f6da8dd96809fa4d0d59d333c2c2662584","target":"record","created_at":"2026-05-18T02:29:54Z","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":"14f2d1f640de31d4e19efc9b3864dc7ff8f6484517862e34a327bb85d26b5892","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-06T22:08:58Z","title_canon_sha256":"ae3f98991214baabb8357ba5052d1eb91b0f8c4af9f1c0df85e4ec526e784370"},"schema_version":"1.0","source":{"id":"1501.01326","kind":"arxiv","version":1}},"canonical_sha256":"fab189b63af7c877bf4cf75a6039bdd921c5f23596b25ef13a05a675b83745fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fab189b63af7c877bf4cf75a6039bdd921c5f23596b25ef13a05a675b83745fe","first_computed_at":"2026-05-18T02:29:54.524603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:54.524603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HZ0vZtitcomEMjtsI89chtvRU/RiVwJbQd7xVox16TGd+DDotrvvQYZn8DCkwn4AbqtpEjkUaX6ABk/6P6LyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:54.525016Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71154be14ba0e8e65bfebe336a14c6f6da8dd96809fa4d0d59d333c2c2662584","sha256:e6bf97a4a80e7f8be12990ccfcd6dd8d8fe92a407f4878f07de21f2c18af8d69"],"state_sha256":"edbda3c0608b5ed11b82d7dd64f682d3e4dd23a3d563003d07a15d0bb1cad597"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UcZVzW6WpH9ST/bkhnZBI9T4b0oMpcPjCjJcVPjQt3f10gQAP8Dsv/J9dpmI7wdSEmO9jEhbZ5jI1Tn1VhZ5AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:54:09.428475Z","bundle_sha256":"ee15e1b157998204a09ee394b9d1ba8aa37916fa99afdd338e8912d47f627818"}}