{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BA4DDYMFUV7IK5UP7ZWBFDSRQF","short_pith_number":"pith:BA4DDYMF","canonical_record":{"source":{"id":"1502.02451","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-09T12:02:32Z","cross_cats_sorted":[],"title_canon_sha256":"234c5019e5c529eb4af2aa344f2e1e3c83e0796ca66c0570a4d3e33a2c951d39","abstract_canon_sha256":"941b46bc2a8673dd1b7f6f13d69a08a57d4969f47e3e051466b72cd9c6bdb697"},"schema_version":"1.0"},"canonical_sha256":"083831e185a57e85768ffe6c128e51816b8c4f1527017e95f8606625f039c946","source":{"kind":"arxiv","id":"1502.02451","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02451","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02451v4","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02451","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"pith_short_12","alias_value":"BA4DDYMFUV7I","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BA4DDYMFUV7IK5UP","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BA4DDYMF","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BA4DDYMFUV7IK5UP7ZWBFDSRQF","target":"record","payload":{"canonical_record":{"source":{"id":"1502.02451","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-09T12:02:32Z","cross_cats_sorted":[],"title_canon_sha256":"234c5019e5c529eb4af2aa344f2e1e3c83e0796ca66c0570a4d3e33a2c951d39","abstract_canon_sha256":"941b46bc2a8673dd1b7f6f13d69a08a57d4969f47e3e051466b72cd9c6bdb697"},"schema_version":"1.0"},"canonical_sha256":"083831e185a57e85768ffe6c128e51816b8c4f1527017e95f8606625f039c946","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:54.102692Z","signature_b64":"BTSl1pRjEdxpBA1Vn8mTLQ8HgZHhsbYEGNCfiEjbWmQXg0cRC2Ausae6snVRdUBaY/SZwyAnwxnMzluGKk8KAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"083831e185a57e85768ffe6c128e51816b8c4f1527017e95f8606625f039c946","last_reissued_at":"2026-05-18T01:04:54.102094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:54.102094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.02451","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jb38c+5qx7VoXstI5kc/XlJhvV+II9aHQkBUSqBSsPT+iwJEniO7lVcnWzGPwK/Z/WNLMhZ3YZHdXRNbL/NTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:28:29.516550Z"},"content_sha256":"e1f886b8263927c030bf356b53ae4db78248eaedc03c9e3a4bda2f8bcf4e4afe","schema_version":"1.0","event_id":"sha256:e1f886b8263927c030bf356b53ae4db78248eaedc03c9e3a4bda2f8bcf4e4afe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BA4DDYMFUV7IK5UP7ZWBFDSRQF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of periodic solutions of the FitzHugh-Nagumo equations for an explicit range of the small parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aleksander Czechowski, Piotr Zgliczy\\'nski","submitted_at":"2015-02-09T12:02:32Z","abstract_excerpt":"The FitzHugh-Nagumo model describing propagation of nerve impulses in axon is given by fast-slow reaction-diffusion equations, with dependence on a parameter $\\epsilon$ representing the ratio of time scales. It is well known that for all sufficiently small $\\epsilon>0$ the system possesses a periodic traveling wave. With aid of computer-assisted rigorous computations, we prove the existence of this periodic orbit in the traveling wave equation for an explicit range $\\epsilon \\in (0, 0.0015]$. Our approach is based on a novel method of combination of topological techniques of covering relations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02451","kind":"arxiv","version":4},"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":"2026-05-18T01:04:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GFBnJzIOQlcbcFLLZut4bk/6sTRPTcZxBgbkb7dz8nf+V9F2QIKtFjCVFT29sfQwSwiyBg42kwpc27qPEHBlAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:28:29.516894Z"},"content_sha256":"3efa1e0ae68dd259e2e05cbddfdb70b903d0ced3720c8d4dc1925e0cce485059","schema_version":"1.0","event_id":"sha256:3efa1e0ae68dd259e2e05cbddfdb70b903d0ced3720c8d4dc1925e0cce485059"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BA4DDYMFUV7IK5UP7ZWBFDSRQF/bundle.json","state_url":"https://pith.science/pith/BA4DDYMFUV7IK5UP7ZWBFDSRQF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BA4DDYMFUV7IK5UP7ZWBFDSRQF/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":"2026-06-06T16:28:29Z","links":{"resolver":"https://pith.science/pith/BA4DDYMFUV7IK5UP7ZWBFDSRQF","bundle":"https://pith.science/pith/BA4DDYMFUV7IK5UP7ZWBFDSRQF/bundle.json","state":"https://pith.science/pith/BA4DDYMFUV7IK5UP7ZWBFDSRQF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BA4DDYMFUV7IK5UP7ZWBFDSRQF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BA4DDYMFUV7IK5UP7ZWBFDSRQF","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":"941b46bc2a8673dd1b7f6f13d69a08a57d4969f47e3e051466b72cd9c6bdb697","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-09T12:02:32Z","title_canon_sha256":"234c5019e5c529eb4af2aa344f2e1e3c83e0796ca66c0570a4d3e33a2c951d39"},"schema_version":"1.0","source":{"id":"1502.02451","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02451","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02451v4","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02451","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"pith_short_12","alias_value":"BA4DDYMFUV7I","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BA4DDYMFUV7IK5UP","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BA4DDYMF","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:3efa1e0ae68dd259e2e05cbddfdb70b903d0ced3720c8d4dc1925e0cce485059","target":"graph","created_at":"2026-05-18T01:04:54Z","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":"The FitzHugh-Nagumo model describing propagation of nerve impulses in axon is given by fast-slow reaction-diffusion equations, with dependence on a parameter $\\epsilon$ representing the ratio of time scales. It is well known that for all sufficiently small $\\epsilon>0$ the system possesses a periodic traveling wave. With aid of computer-assisted rigorous computations, we prove the existence of this periodic orbit in the traveling wave equation for an explicit range $\\epsilon \\in (0, 0.0015]$. Our approach is based on a novel method of combination of topological techniques of covering relations","authors_text":"Aleksander Czechowski, Piotr Zgliczy\\'nski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-09T12:02:32Z","title":"Existence of periodic solutions of the FitzHugh-Nagumo equations for an explicit range of the small parameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02451","kind":"arxiv","version":4},"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:e1f886b8263927c030bf356b53ae4db78248eaedc03c9e3a4bda2f8bcf4e4afe","target":"record","created_at":"2026-05-18T01:04:54Z","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":"941b46bc2a8673dd1b7f6f13d69a08a57d4969f47e3e051466b72cd9c6bdb697","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-09T12:02:32Z","title_canon_sha256":"234c5019e5c529eb4af2aa344f2e1e3c83e0796ca66c0570a4d3e33a2c951d39"},"schema_version":"1.0","source":{"id":"1502.02451","kind":"arxiv","version":4}},"canonical_sha256":"083831e185a57e85768ffe6c128e51816b8c4f1527017e95f8606625f039c946","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"083831e185a57e85768ffe6c128e51816b8c4f1527017e95f8606625f039c946","first_computed_at":"2026-05-18T01:04:54.102094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:54.102094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BTSl1pRjEdxpBA1Vn8mTLQ8HgZHhsbYEGNCfiEjbWmQXg0cRC2Ausae6snVRdUBaY/SZwyAnwxnMzluGKk8KAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:54.102692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02451","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1f886b8263927c030bf356b53ae4db78248eaedc03c9e3a4bda2f8bcf4e4afe","sha256:3efa1e0ae68dd259e2e05cbddfdb70b903d0ced3720c8d4dc1925e0cce485059"],"state_sha256":"c8d153595035eeaaef06f673c8249e6a48ac7897ab956afa144ff5f652680540"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C1j8oXDqkKSGtoZZoaB3Fdpi1Jx+0bLFWdSpPOG/gpDGxb6+Zu429s6PhMDS9BjlX3FrvZ4CSgxpduUt2zlwCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:28:29.519108Z","bundle_sha256":"161613b57e7e8ec27c9e496c0b2b4325a9c2bb1e27c48499da325593d5fee710"}}