{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XRGC7XBXCDLNVDEQ5EIYCMBQPT","short_pith_number":"pith:XRGC7XBX","canonical_record":{"source":{"id":"1611.03237","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T09:48:37Z","cross_cats_sorted":[],"title_canon_sha256":"5bab578e26511d6ddba99972ede7ca9cf35178a3e2dd314c023533d5a8466376","abstract_canon_sha256":"85da726196c80281d62bdd69c3544a7391ef70bc7e0b0385d810883289ab8ea3"},"schema_version":"1.0"},"canonical_sha256":"bc4c2fdc3710d6da8c90e9118130307cee55619a7ecfc6b98f17b88e1804428b","source":{"kind":"arxiv","id":"1611.03237","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03237","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03237v2","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03237","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"pith_short_12","alias_value":"XRGC7XBXCDLN","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XRGC7XBXCDLNVDEQ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XRGC7XBX","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XRGC7XBXCDLNVDEQ5EIYCMBQPT","target":"record","payload":{"canonical_record":{"source":{"id":"1611.03237","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T09:48:37Z","cross_cats_sorted":[],"title_canon_sha256":"5bab578e26511d6ddba99972ede7ca9cf35178a3e2dd314c023533d5a8466376","abstract_canon_sha256":"85da726196c80281d62bdd69c3544a7391ef70bc7e0b0385d810883289ab8ea3"},"schema_version":"1.0"},"canonical_sha256":"bc4c2fdc3710d6da8c90e9118130307cee55619a7ecfc6b98f17b88e1804428b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:02.607631Z","signature_b64":"N3ulwV4V26CRBZ3rB6cTjGizJm36MEZnxIp3YRElDUHYKFz68TzSjzLg7wi1XnjKD/EDje+pAIkvvlmk1XeLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc4c2fdc3710d6da8c90e9118130307cee55619a7ecfc6b98f17b88e1804428b","last_reissued_at":"2026-05-18T00:28:02.607085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:02.607085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.03237","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:28:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7tKmJm9GJB8Q4/Jqn99wMnqHa2g1N09GkT7SDMsY0uhG7Eqko7jDh4bep6OE5dfWuJSaIUTzK37K0DlK2zHgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:53:28.894934Z"},"content_sha256":"a0d6158477f2be856b50d1b79bc7d12e08136c6f38aabdec343282e3c1ae9c10","schema_version":"1.0","event_id":"sha256:a0d6158477f2be856b50d1b79bc7d12e08136c6f38aabdec343282e3c1ae9c10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XRGC7XBXCDLNVDEQ5EIYCMBQPT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Competition in periodic media: II -- Segregative limit of pulsating fronts and \"Unity is not Strength\"-type result","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gr\\'egoire Nadin (LJLL), L\\'eo Girardin (LJLL)","submitted_at":"2016-11-10T09:48:37Z","abstract_excerpt":"This paper is concerned with the limit, as the interspecific competition rate goes to infinity, of pulsating front solutions in space-periodic media for a bistable two-species competition--diffusion Lotka--Volterra system. We distinguish two important cases: null asymptotic speed and non-null as-ymptotic speed. In the former case, we show the existence of a segregated stationary equilibrium. In the latter case, we are able to uniquely characterize the segregated pulsating front, and thus full convergence is proved. The segregated pulsating front solves an interesting free boundary problem. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03237","kind":"arxiv","version":2},"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":"2026-05-18T00:28:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wBKgQQ+xr8S8nefmAk6CReAqQFYHfZveyJGaqvf23SeGzCAXhtMAw1T5HIhdPcX6wEOCEYgMaCofsrO8QxQNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:53:28.895297Z"},"content_sha256":"26e5ffcaf367eb04b02ee27172d5826fe01040a4a96bdf54693ca398c199c7c4","schema_version":"1.0","event_id":"sha256:26e5ffcaf367eb04b02ee27172d5826fe01040a4a96bdf54693ca398c199c7c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XRGC7XBXCDLNVDEQ5EIYCMBQPT/bundle.json","state_url":"https://pith.science/pith/XRGC7XBXCDLNVDEQ5EIYCMBQPT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XRGC7XBXCDLNVDEQ5EIYCMBQPT/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":"2026-07-01T07:53:28Z","links":{"resolver":"https://pith.science/pith/XRGC7XBXCDLNVDEQ5EIYCMBQPT","bundle":"https://pith.science/pith/XRGC7XBXCDLNVDEQ5EIYCMBQPT/bundle.json","state":"https://pith.science/pith/XRGC7XBXCDLNVDEQ5EIYCMBQPT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XRGC7XBXCDLNVDEQ5EIYCMBQPT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XRGC7XBXCDLNVDEQ5EIYCMBQPT","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":"85da726196c80281d62bdd69c3544a7391ef70bc7e0b0385d810883289ab8ea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T09:48:37Z","title_canon_sha256":"5bab578e26511d6ddba99972ede7ca9cf35178a3e2dd314c023533d5a8466376"},"schema_version":"1.0","source":{"id":"1611.03237","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03237","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03237v2","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03237","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"pith_short_12","alias_value":"XRGC7XBXCDLN","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XRGC7XBXCDLNVDEQ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XRGC7XBX","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:26e5ffcaf367eb04b02ee27172d5826fe01040a4a96bdf54693ca398c199c7c4","target":"graph","created_at":"2026-05-18T00:28:02Z","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":"This paper is concerned with the limit, as the interspecific competition rate goes to infinity, of pulsating front solutions in space-periodic media for a bistable two-species competition--diffusion Lotka--Volterra system. We distinguish two important cases: null asymptotic speed and non-null as-ymptotic speed. In the former case, we show the existence of a segregated stationary equilibrium. In the latter case, we are able to uniquely characterize the segregated pulsating front, and thus full convergence is proved. The segregated pulsating front solves an interesting free boundary problem. We ","authors_text":"Gr\\'egoire Nadin (LJLL), L\\'eo Girardin (LJLL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T09:48:37Z","title":"Competition in periodic media: II -- Segregative limit of pulsating fronts and \"Unity is not Strength\"-type result"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03237","kind":"arxiv","version":2},"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:a0d6158477f2be856b50d1b79bc7d12e08136c6f38aabdec343282e3c1ae9c10","target":"record","created_at":"2026-05-18T00:28:02Z","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":"85da726196c80281d62bdd69c3544a7391ef70bc7e0b0385d810883289ab8ea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T09:48:37Z","title_canon_sha256":"5bab578e26511d6ddba99972ede7ca9cf35178a3e2dd314c023533d5a8466376"},"schema_version":"1.0","source":{"id":"1611.03237","kind":"arxiv","version":2}},"canonical_sha256":"bc4c2fdc3710d6da8c90e9118130307cee55619a7ecfc6b98f17b88e1804428b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc4c2fdc3710d6da8c90e9118130307cee55619a7ecfc6b98f17b88e1804428b","first_computed_at":"2026-05-18T00:28:02.607085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:02.607085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N3ulwV4V26CRBZ3rB6cTjGizJm36MEZnxIp3YRElDUHYKFz68TzSjzLg7wi1XnjKD/EDje+pAIkvvlmk1XeLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:02.607631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03237","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0d6158477f2be856b50d1b79bc7d12e08136c6f38aabdec343282e3c1ae9c10","sha256:26e5ffcaf367eb04b02ee27172d5826fe01040a4a96bdf54693ca398c199c7c4"],"state_sha256":"09d5fbe79c4b325b3afb8931ceff5f9b7ecedadd84e99ec3e3c6861b6557f420"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nV3BRXHBZcOeOZwSUceGD/1WFGEE0QDDi76blaIXpQY/712TVggez/Jd5IxbYnvxnZCD+2JcRBgmeZP891QKCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T07:53:28.897824Z","bundle_sha256":"33d317c6866fd11f8a80aa4f0a542b2d787c7480424703f3cb93873fca519a81"}}