{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:A5SAFE6ZIMCS4XJQNO3RIXAK4W","short_pith_number":"pith:A5SAFE6Z","canonical_record":{"source":{"id":"1505.04626","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-18T13:16:17Z","cross_cats_sorted":[],"title_canon_sha256":"78c4e01241efa16e6bf7841b44ca9886eabac0a3b611c113d25fdb58e553827c","abstract_canon_sha256":"be2d0d2faa821755bfb7a1df74e2b86edc5a2740db38f89ec14fcd991724fc47"},"schema_version":"1.0"},"canonical_sha256":"07640293d943052e5d306bb7145c0ae5bab119eb2f4b3a2f8eb1ffa5e4e531dc","source":{"kind":"arxiv","id":"1505.04626","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04626","created_at":"2026-05-18T02:07:24Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04626v1","created_at":"2026-05-18T02:07:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04626","created_at":"2026-05-18T02:07:24Z"},{"alias_kind":"pith_short_12","alias_value":"A5SAFE6ZIMCS","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A5SAFE6ZIMCS4XJQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A5SAFE6Z","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:A5SAFE6ZIMCS4XJQNO3RIXAK4W","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04626","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-18T13:16:17Z","cross_cats_sorted":[],"title_canon_sha256":"78c4e01241efa16e6bf7841b44ca9886eabac0a3b611c113d25fdb58e553827c","abstract_canon_sha256":"be2d0d2faa821755bfb7a1df74e2b86edc5a2740db38f89ec14fcd991724fc47"},"schema_version":"1.0"},"canonical_sha256":"07640293d943052e5d306bb7145c0ae5bab119eb2f4b3a2f8eb1ffa5e4e531dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:24.973261Z","signature_b64":"ySah3ozcnyLxAjsJqRTdom6Cz3U1/KobJd2Iml5B0Rfz5aSVHRmN3ZahRN2N4d+VGHJIuG+MFkPltMw0RjB0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07640293d943052e5d306bb7145c0ae5bab119eb2f4b3a2f8eb1ffa5e4e531dc","last_reissued_at":"2026-05-18T02:07:24.972873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:24.972873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04626","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":"2026-05-18T02:07:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vbqS7CH50RHshL3g+YO7G4ZS8NuXIXJFiVQsDr0FYQVYiK2fb0FPmzIwujKJ50ENkqx1y3Z8BqmHxEUXrpkQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:54:25.062547Z"},"content_sha256":"c61a3712c5c1b5333d856c7100f3a6a34410347f70984619d7d96b9d998e243c","schema_version":"1.0","event_id":"sha256:c61a3712c5c1b5333d856c7100f3a6a34410347f70984619d7d96b9d998e243c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:A5SAFE6ZIMCS4XJQNO3RIXAK4W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Slowing Allee effect vs. accelerating heavy tails in monostable reaction diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Matthieu Alfaro (I3M)","submitted_at":"2015-05-18T13:16:17Z","abstract_excerpt":"We focus on the spreading properties of solutions of monostable reaction-diffusion equations. Initial data are assumed to have heavy tails, which tends to accelerate the invasion phenomenon. On the other hand, the nonlinearity involves a weak Allee effect, which tends to slow down the process. We study the balance between the two effects. For algebraic tails, we prove the exact separation between \"no acceleration and acceleration\". This implies in particular that, for tails exponentially unbounded but lighter than algebraic , acceleration never occurs in presence of an Allee effect. This is in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04626","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":"2026-05-18T02:07:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vr68KJnpiBv1O9aSaPLOz89cDDfW32j6Y6y8vOpYdVMn1aKXeGHValtQfqSD7pwq4pRtOZ524sBIO55gIcZBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:54:25.062892Z"},"content_sha256":"496a2cfdca00ca97010a84cc75cbbfe18932d36b193e7f244530c36016a8896e","schema_version":"1.0","event_id":"sha256:496a2cfdca00ca97010a84cc75cbbfe18932d36b193e7f244530c36016a8896e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A5SAFE6ZIMCS4XJQNO3RIXAK4W/bundle.json","state_url":"https://pith.science/pith/A5SAFE6ZIMCS4XJQNO3RIXAK4W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A5SAFE6ZIMCS4XJQNO3RIXAK4W/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":"2026-06-25T06:54:25Z","links":{"resolver":"https://pith.science/pith/A5SAFE6ZIMCS4XJQNO3RIXAK4W","bundle":"https://pith.science/pith/A5SAFE6ZIMCS4XJQNO3RIXAK4W/bundle.json","state":"https://pith.science/pith/A5SAFE6ZIMCS4XJQNO3RIXAK4W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A5SAFE6ZIMCS4XJQNO3RIXAK4W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:A5SAFE6ZIMCS4XJQNO3RIXAK4W","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":"be2d0d2faa821755bfb7a1df74e2b86edc5a2740db38f89ec14fcd991724fc47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-18T13:16:17Z","title_canon_sha256":"78c4e01241efa16e6bf7841b44ca9886eabac0a3b611c113d25fdb58e553827c"},"schema_version":"1.0","source":{"id":"1505.04626","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04626","created_at":"2026-05-18T02:07:24Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04626v1","created_at":"2026-05-18T02:07:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04626","created_at":"2026-05-18T02:07:24Z"},{"alias_kind":"pith_short_12","alias_value":"A5SAFE6ZIMCS","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A5SAFE6ZIMCS4XJQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A5SAFE6Z","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:496a2cfdca00ca97010a84cc75cbbfe18932d36b193e7f244530c36016a8896e","target":"graph","created_at":"2026-05-18T02:07:24Z","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":"We focus on the spreading properties of solutions of monostable reaction-diffusion equations. Initial data are assumed to have heavy tails, which tends to accelerate the invasion phenomenon. On the other hand, the nonlinearity involves a weak Allee effect, which tends to slow down the process. We study the balance between the two effects. For algebraic tails, we prove the exact separation between \"no acceleration and acceleration\". This implies in particular that, for tails exponentially unbounded but lighter than algebraic , acceleration never occurs in presence of an Allee effect. This is in","authors_text":"Matthieu Alfaro (I3M)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-18T13:16:17Z","title":"Slowing Allee effect vs. accelerating heavy tails in monostable reaction diffusion equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04626","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:c61a3712c5c1b5333d856c7100f3a6a34410347f70984619d7d96b9d998e243c","target":"record","created_at":"2026-05-18T02:07:24Z","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":"be2d0d2faa821755bfb7a1df74e2b86edc5a2740db38f89ec14fcd991724fc47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-18T13:16:17Z","title_canon_sha256":"78c4e01241efa16e6bf7841b44ca9886eabac0a3b611c113d25fdb58e553827c"},"schema_version":"1.0","source":{"id":"1505.04626","kind":"arxiv","version":1}},"canonical_sha256":"07640293d943052e5d306bb7145c0ae5bab119eb2f4b3a2f8eb1ffa5e4e531dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07640293d943052e5d306bb7145c0ae5bab119eb2f4b3a2f8eb1ffa5e4e531dc","first_computed_at":"2026-05-18T02:07:24.972873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:24.972873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ySah3ozcnyLxAjsJqRTdom6Cz3U1/KobJd2Iml5B0Rfz5aSVHRmN3ZahRN2N4d+VGHJIuG+MFkPltMw0RjB0DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:24.973261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04626","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c61a3712c5c1b5333d856c7100f3a6a34410347f70984619d7d96b9d998e243c","sha256:496a2cfdca00ca97010a84cc75cbbfe18932d36b193e7f244530c36016a8896e"],"state_sha256":"59cf53a3a7d9b920b1cb358254a8d913bd79d2d96d0125a63211aa8f241129d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zwVlgJ6vnb9qFYj9XsVMS3v3LfbyDeqjjtYdCre+NZHPpq6bmVNmFZcJhHw39IMeeix8GToPPUaRRHg9crE2Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T06:54:25.064892Z","bundle_sha256":"d0bc34fe32ceabbbe514f43cff78b19b0b68cdd20a7d0894436458540d8ac2f4"}}