{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Q3XSUGBBEVXHEQXMRTDBECIFNU","short_pith_number":"pith:Q3XSUGBB","canonical_record":{"source":{"id":"1305.5573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-23T21:47:13Z","cross_cats_sorted":[],"title_canon_sha256":"245df0ef5db6241fc09bfe867a5ac5be7ed91ee4ce640955d421f33aa3d584be","abstract_canon_sha256":"21f57b2b02bdf6c3035fd5bef5d3db9aacd9ada6cf209f74ffcca6d39c85bb84"},"schema_version":"1.0"},"canonical_sha256":"86ef2a1821256e7242ec8cc61209056d066e1114d84f9010df1867e0ba307e6a","source":{"kind":"arxiv","id":"1305.5573","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5573","created_at":"2026-05-18T01:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5573v1","created_at":"2026-05-18T01:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5573","created_at":"2026-05-18T01:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"Q3XSUGBBEVXH","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q3XSUGBBEVXHEQXM","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q3XSUGBB","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Q3XSUGBBEVXHEQXMRTDBECIFNU","target":"record","payload":{"canonical_record":{"source":{"id":"1305.5573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-23T21:47:13Z","cross_cats_sorted":[],"title_canon_sha256":"245df0ef5db6241fc09bfe867a5ac5be7ed91ee4ce640955d421f33aa3d584be","abstract_canon_sha256":"21f57b2b02bdf6c3035fd5bef5d3db9aacd9ada6cf209f74ffcca6d39c85bb84"},"schema_version":"1.0"},"canonical_sha256":"86ef2a1821256e7242ec8cc61209056d066e1114d84f9010df1867e0ba307e6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:13.011079Z","signature_b64":"/bzxuwebdwJtxNFGL1dgP+nwMDKYggawQ3uRMhmtckQBGyFdjDbSpQKCuU0VCvtaC3kkX3NfwzZS+gu4qnjOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86ef2a1821256e7242ec8cc61209056d066e1114d84f9010df1867e0ba307e6a","last_reissued_at":"2026-05-18T01:17:13.010372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:13.010372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.5573","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":"2026-05-18T01:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DnL94g/6azRYUd4MM+DeiOdbDaPNJ2+cUtYO5OR0YYaQHsu4NIUXg4ireSpflmNokqG+lQZVIxnCSoYvIwLyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:57:49.692401Z"},"content_sha256":"c92b5b5aef6dd5fea0e7a5982a9ed0a65b3423b8c0a637ceb59421a9027040be","schema_version":"1.0","event_id":"sha256:c92b5b5aef6dd5fea0e7a5982a9ed0a65b3423b8c0a637ceb59421a9027040be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Q3XSUGBBEVXHEQXMRTDBECIFNU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A two end family of solutions for the Inhomogeneous Allen-Cahn equation in R^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andres Zuniga, Oscar Agudelo","submitted_at":"2013-05-23T21:47:13Z","abstract_excerpt":"In this work we construct a family of entire bounded solution for the singulary perturbed Inhomogeneous Allen-Cahn Equation $\\ep^2\\div\\left(a(x)\\nabla u\\right)-a(x)F'(u)=0$ in $\\R^2$, where $\\ep\\to 0$. The nodal set of these solutions is close to a \"nondegenerate\" curve which is asymptotically two non paralell straight lines. Here $F'$ is a double-well potential and $a$ is a smooth positive function. We also provide example of curves and functions $a$ where our result applies. This work is in connection with the results found by Z.Du and B.Lai, Z.Du and C.Gui, and F. Pacard and M. Ritore, in \""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5573","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":"2026-05-18T01:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PX66DkZNlmStUrnpEz1kqZ4P5fqqWZQnECUf+RRoBGA/v6MVqOZ4U6lKyrVJz+fFi7Qu5OTtG6jVXLEd4JWpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:57:49.692742Z"},"content_sha256":"06949ed9c1a5aadedbd6afe5556dcec339e2a4f04e263851da72562ddd3f8491","schema_version":"1.0","event_id":"sha256:06949ed9c1a5aadedbd6afe5556dcec339e2a4f04e263851da72562ddd3f8491"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3XSUGBBEVXHEQXMRTDBECIFNU/bundle.json","state_url":"https://pith.science/pith/Q3XSUGBBEVXHEQXMRTDBECIFNU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3XSUGBBEVXHEQXMRTDBECIFNU/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":"2026-06-20T14:57:49Z","links":{"resolver":"https://pith.science/pith/Q3XSUGBBEVXHEQXMRTDBECIFNU","bundle":"https://pith.science/pith/Q3XSUGBBEVXHEQXMRTDBECIFNU/bundle.json","state":"https://pith.science/pith/Q3XSUGBBEVXHEQXMRTDBECIFNU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3XSUGBBEVXHEQXMRTDBECIFNU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q3XSUGBBEVXHEQXMRTDBECIFNU","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":"21f57b2b02bdf6c3035fd5bef5d3db9aacd9ada6cf209f74ffcca6d39c85bb84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-23T21:47:13Z","title_canon_sha256":"245df0ef5db6241fc09bfe867a5ac5be7ed91ee4ce640955d421f33aa3d584be"},"schema_version":"1.0","source":{"id":"1305.5573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5573","created_at":"2026-05-18T01:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5573v1","created_at":"2026-05-18T01:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5573","created_at":"2026-05-18T01:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"Q3XSUGBBEVXH","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q3XSUGBBEVXHEQXM","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q3XSUGBB","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:06949ed9c1a5aadedbd6afe5556dcec339e2a4f04e263851da72562ddd3f8491","target":"graph","created_at":"2026-05-18T01:17:13Z","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 work we construct a family of entire bounded solution for the singulary perturbed Inhomogeneous Allen-Cahn Equation $\\ep^2\\div\\left(a(x)\\nabla u\\right)-a(x)F'(u)=0$ in $\\R^2$, where $\\ep\\to 0$. The nodal set of these solutions is close to a \"nondegenerate\" curve which is asymptotically two non paralell straight lines. Here $F'$ is a double-well potential and $a$ is a smooth positive function. We also provide example of curves and functions $a$ where our result applies. This work is in connection with the results found by Z.Du and B.Lai, Z.Du and C.Gui, and F. Pacard and M. Ritore, in \"","authors_text":"Andres Zuniga, Oscar Agudelo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-23T21:47:13Z","title":"A two end family of solutions for the Inhomogeneous Allen-Cahn equation in R^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5573","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:c92b5b5aef6dd5fea0e7a5982a9ed0a65b3423b8c0a637ceb59421a9027040be","target":"record","created_at":"2026-05-18T01:17:13Z","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":"21f57b2b02bdf6c3035fd5bef5d3db9aacd9ada6cf209f74ffcca6d39c85bb84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-23T21:47:13Z","title_canon_sha256":"245df0ef5db6241fc09bfe867a5ac5be7ed91ee4ce640955d421f33aa3d584be"},"schema_version":"1.0","source":{"id":"1305.5573","kind":"arxiv","version":1}},"canonical_sha256":"86ef2a1821256e7242ec8cc61209056d066e1114d84f9010df1867e0ba307e6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86ef2a1821256e7242ec8cc61209056d066e1114d84f9010df1867e0ba307e6a","first_computed_at":"2026-05-18T01:17:13.010372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:13.010372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/bzxuwebdwJtxNFGL1dgP+nwMDKYggawQ3uRMhmtckQBGyFdjDbSpQKCuU0VCvtaC3kkX3NfwzZS+gu4qnjOAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:13.011079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c92b5b5aef6dd5fea0e7a5982a9ed0a65b3423b8c0a637ceb59421a9027040be","sha256:06949ed9c1a5aadedbd6afe5556dcec339e2a4f04e263851da72562ddd3f8491"],"state_sha256":"5443b7f2f9feebd33b8c3924b7ac753612fb0e1d9ad7851e116292310de949ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wuiZNZ1ohQJ2TJlkhEHdwr0ODuDoUZkEFjJfTMb24HHBtCCkGZayhE1zUhwfsbVCRc73whJONHUNKZqt9iWpDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T14:57:49.694577Z","bundle_sha256":"ad81c4f8125593d6bfc56f093dc52bc595a28e9ec2a3e94e9c01ab5ad6fdf7c6"}}