{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HQORZXDRFTRBFTHNWBKOFLPDWC","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":"cf6dd911a6eab80cb8abcdd8d0af66aaeeef8389ad75673ce13f88024a9850bd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-08T16:11:18Z","title_canon_sha256":"48545c697d1f9f532a149434efe6ce16ffc82b14c7c02524a1fc071d2b598fd8"},"schema_version":"1.0","source":{"id":"1805.03133","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03133","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03133v3","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03133","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"HQORZXDRFTRB","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HQORZXDRFTRBFTHN","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HQORZXDR","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:9e85c27111eafaea77cac906f1cd17f1fc6f37d37c433fface55914f226f933f","target":"graph","created_at":"2026-05-17T23:40:41Z","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":"Symmetric random walks in $R^d$ and $Z^d$ are considered. It is assumed that the jump distribution density has moderate tails, i.e., several density moments are finite, including the second one. The global (for all $x$ and $t$) asymptotic behavior at infinity of the transition probability (fundamental solution of the corresponding parabolic convolution operator) is found. Front propagation of ecological waves in the corresponding population dynamics models is described.","authors_text":"B. Vainberg, S. Molchanov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-08T16:11:18Z","title":"Population dynamics with moderate tails of the underlying random walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03133","kind":"arxiv","version":3},"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":"sha256:9302595d2a9ca5f8b032adb5a5fa47783cea68c8ff65411b87fb1c53c6c1c06d","target":"record","created_at":"2026-05-17T23:40:41Z","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":"cf6dd911a6eab80cb8abcdd8d0af66aaeeef8389ad75673ce13f88024a9850bd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-08T16:11:18Z","title_canon_sha256":"48545c697d1f9f532a149434efe6ce16ffc82b14c7c02524a1fc071d2b598fd8"},"schema_version":"1.0","source":{"id":"1805.03133","kind":"arxiv","version":3}},"canonical_sha256":"3c1d1cdc712ce212ccedb054e2ade3b0924af669304879d87aeff7fcc965ae62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c1d1cdc712ce212ccedb054e2ade3b0924af669304879d87aeff7fcc965ae62","first_computed_at":"2026-05-17T23:40:41.811198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:41.811198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UylVQoo+g1qBwqHVYvv1YQZsgCyRxvuiVyY77/CTFc9EfNE4JHM3adr5wiIGlX5fI8Vvy5KXRmRKUdsxSLixCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:41.811652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.03133","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9302595d2a9ca5f8b032adb5a5fa47783cea68c8ff65411b87fb1c53c6c1c06d","sha256:9e85c27111eafaea77cac906f1cd17f1fc6f37d37c433fface55914f226f933f"],"state_sha256":"c65e83038b5cedc75c6c6c6ed7f6679c3cff0e22d2d5d2e9ed07bbe1e227ec5b"}