{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6TF5BPCNBVQDB3SJWZGJRPCM44","short_pith_number":"pith:6TF5BPCN","canonical_record":{"source":{"id":"1511.01414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-04T17:47:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"42d88354264fa41954237b8b1c8f9a5d43a3f8d40fd764e0c2afcf7c80e80c3a","abstract_canon_sha256":"12382adfcd1e02099fd81cedeae00676797de11b7988fce56762ca9557492694"},"schema_version":"1.0"},"canonical_sha256":"f4cbd0bc4d0d6030ee49b64c98bc4ce738dd20d1f949adec67826e3a9a085b18","source":{"kind":"arxiv","id":"1511.01414","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01414","created_at":"2026-05-18T01:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01414v1","created_at":"2026-05-18T01:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01414","created_at":"2026-05-18T01:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"6TF5BPCNBVQD","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6TF5BPCNBVQDB3SJ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6TF5BPCN","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6TF5BPCNBVQDB3SJWZGJRPCM44","target":"record","payload":{"canonical_record":{"source":{"id":"1511.01414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-04T17:47:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"42d88354264fa41954237b8b1c8f9a5d43a3f8d40fd764e0c2afcf7c80e80c3a","abstract_canon_sha256":"12382adfcd1e02099fd81cedeae00676797de11b7988fce56762ca9557492694"},"schema_version":"1.0"},"canonical_sha256":"f4cbd0bc4d0d6030ee49b64c98bc4ce738dd20d1f949adec67826e3a9a085b18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:47.149698Z","signature_b64":"4gRWTt//nNlaTN6P1aaRUUTimlzw4oZSOrAPd06WYAZ56nB3yldlmrmqX/FHHTdMmXzBg0cmnP73Eg2Y2mxLCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4cbd0bc4d0d6030ee49b64c98bc4ce738dd20d1f949adec67826e3a9a085b18","last_reissued_at":"2026-05-18T01:27:47.149154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:47.149154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.01414","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":"2026-05-18T01:27:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GUwzaSGh84hxaZ0/Gqr6FfJgXJFuuejgbk3PAIFh7TdzI0zwDtPWZcwNcfvbvSJsmX2SxVwze7rXu3YeP0KYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:57:08.386841Z"},"content_sha256":"cf93dcdc9575dcbb99a0cd2f328cba6672dfc8ca34e1ff568d0eb2e66d3ec887","schema_version":"1.0","event_id":"sha256:cf93dcdc9575dcbb99a0cd2f328cba6672dfc8ca34e1ff568d0eb2e66d3ec887"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6TF5BPCNBVQDB3SJWZGJRPCM44","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global bifurcation diagram of steady states of systems of PDEs via rigorous numerics: a 3-component reaction-diffusion system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Jean-Philippe Lessard, Matthieu Vanicat, Maxime Breden","submitted_at":"2015-11-04T17:47:15Z","abstract_excerpt":"In this paper, we use rigorous numerics to compute several global smooth branches of steady states for a system of three reaction-diffusion PDEs introduced by Iida et al. [J. Math. Biol., {\\bf 53}, 617--641 (2006)] to study the effect of cross-diffusion in competitive interactions. An explicit and mathematically rigorous construction of a global bifurcation diagram is done, except in small neighborhoods of the bifurcations. The proposed method, even though influenced by the work of van den Berg et al. [Math. Comp., {\\bf 79}, 1565--1584 (2010)], introduces new analytic estimates, a new {\\em glu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01414","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":"2026-05-18T01:27:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4zHmhi1ikR/QIPHeumMIddWA/J8TcFAEQQQbGvVsI/tiRd64ABv8KxEHbMv7SnPMFxn0GVkrc22s8WJpPrReAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:57:08.387179Z"},"content_sha256":"0076e56d22b6f037207a2c1a8f965d1634bbce78cc94131c04e8c2b4a6104d41","schema_version":"1.0","event_id":"sha256:0076e56d22b6f037207a2c1a8f965d1634bbce78cc94131c04e8c2b4a6104d41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6TF5BPCNBVQDB3SJWZGJRPCM44/bundle.json","state_url":"https://pith.science/pith/6TF5BPCNBVQDB3SJWZGJRPCM44/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6TF5BPCNBVQDB3SJWZGJRPCM44/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":"2026-06-02T22:57:08Z","links":{"resolver":"https://pith.science/pith/6TF5BPCNBVQDB3SJWZGJRPCM44","bundle":"https://pith.science/pith/6TF5BPCNBVQDB3SJWZGJRPCM44/bundle.json","state":"https://pith.science/pith/6TF5BPCNBVQDB3SJWZGJRPCM44/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6TF5BPCNBVQDB3SJWZGJRPCM44/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6TF5BPCNBVQDB3SJWZGJRPCM44","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":"12382adfcd1e02099fd81cedeae00676797de11b7988fce56762ca9557492694","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-04T17:47:15Z","title_canon_sha256":"42d88354264fa41954237b8b1c8f9a5d43a3f8d40fd764e0c2afcf7c80e80c3a"},"schema_version":"1.0","source":{"id":"1511.01414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01414","created_at":"2026-05-18T01:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01414v1","created_at":"2026-05-18T01:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01414","created_at":"2026-05-18T01:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"6TF5BPCNBVQD","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6TF5BPCNBVQDB3SJ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6TF5BPCN","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:0076e56d22b6f037207a2c1a8f965d1634bbce78cc94131c04e8c2b4a6104d41","target":"graph","created_at":"2026-05-18T01:27:47Z","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 use rigorous numerics to compute several global smooth branches of steady states for a system of three reaction-diffusion PDEs introduced by Iida et al. [J. Math. Biol., {\\bf 53}, 617--641 (2006)] to study the effect of cross-diffusion in competitive interactions. An explicit and mathematically rigorous construction of a global bifurcation diagram is done, except in small neighborhoods of the bifurcations. The proposed method, even though influenced by the work of van den Berg et al. [Math. Comp., {\\bf 79}, 1565--1584 (2010)], introduces new analytic estimates, a new {\\em glu","authors_text":"Jean-Philippe Lessard, Matthieu Vanicat, Maxime Breden","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-04T17:47:15Z","title":"Global bifurcation diagram of steady states of systems of PDEs via rigorous numerics: a 3-component reaction-diffusion system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01414","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:cf93dcdc9575dcbb99a0cd2f328cba6672dfc8ca34e1ff568d0eb2e66d3ec887","target":"record","created_at":"2026-05-18T01:27:47Z","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":"12382adfcd1e02099fd81cedeae00676797de11b7988fce56762ca9557492694","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-04T17:47:15Z","title_canon_sha256":"42d88354264fa41954237b8b1c8f9a5d43a3f8d40fd764e0c2afcf7c80e80c3a"},"schema_version":"1.0","source":{"id":"1511.01414","kind":"arxiv","version":1}},"canonical_sha256":"f4cbd0bc4d0d6030ee49b64c98bc4ce738dd20d1f949adec67826e3a9a085b18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4cbd0bc4d0d6030ee49b64c98bc4ce738dd20d1f949adec67826e3a9a085b18","first_computed_at":"2026-05-18T01:27:47.149154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:47.149154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4gRWTt//nNlaTN6P1aaRUUTimlzw4oZSOrAPd06WYAZ56nB3yldlmrmqX/FHHTdMmXzBg0cmnP73Eg2Y2mxLCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:47.149698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf93dcdc9575dcbb99a0cd2f328cba6672dfc8ca34e1ff568d0eb2e66d3ec887","sha256:0076e56d22b6f037207a2c1a8f965d1634bbce78cc94131c04e8c2b4a6104d41"],"state_sha256":"1fb9d298f01d69b75956c6fbbc8826d3b2b1f2e7edf169c415b8de29a3c16a51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ph94GfQXAdzu7LeKdAj0THBHrEmsje5FDDOlL+GUpPyrtghQuHcxEPwi6wBefEWTQFUxN/89eBqsimIEUNLPCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:57:08.389059Z","bundle_sha256":"3d80124a9a63741801cf1eb4f097870e81e37a38518695f43d010299b54e13ce"}}