{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JQAUZSOAPZQMNKEVF6PD2AA7LR","short_pith_number":"pith:JQAUZSOA","schema_version":"1.0","canonical_sha256":"4c014cc9c07e60c6a8952f9e3d001f5c4a4723025a448266d63de0953b49b564","source":{"kind":"arxiv","id":"1610.06877","version":3},"attestation_state":"computed","paper":{"title":"Invasion fronts on graphs: the Fisher-KPP equation on homogeneous trees and Erd\\H{o}s-R\\'eyni graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Aaron Hoffman, Matt Holzer","submitted_at":"2016-10-21T17:49:54Z","abstract_excerpt":"We study the dynamics of the Fisher-KPP equation on the infinite homogeneous tree and Erd\\H{o}s-R\\'eyni random graphs. We assume initial data that is zero everywhere except at a single node. For the case of the homogeneous tree, the solution will either form a traveling front or converge pointwise to zero. This dichotomy is determined by the linear spreading speed and we compute critical values of the diffusion parameter for which the spreading speed is zero and maximal and prove that the system is linearly determined. We also study the growth of the total population in the network and identif"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.06877","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-10-21T17:49:54Z","cross_cats_sorted":[],"title_canon_sha256":"058666d97a47ab457909aa9227a92ee839c347b77f8e031a43596bbbdf833f4a","abstract_canon_sha256":"065359da360fd29d4311a2a63aba029a7fdd298651f0710348dad67173400d5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:56.756734Z","signature_b64":"GQ1O3K1704JgpFTzt7VNNGaHiuNx1xn5YwPzI4maE9ci4ww9cCGwQN3trhQEWuwuSyFD0GIhWVKmyrZpOqCVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c014cc9c07e60c6a8952f9e3d001f5c4a4723025a448266d63de0953b49b564","last_reissued_at":"2026-05-18T00:16:56.756037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:56.756037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invasion fronts on graphs: the Fisher-KPP equation on homogeneous trees and Erd\\H{o}s-R\\'eyni graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Aaron Hoffman, Matt Holzer","submitted_at":"2016-10-21T17:49:54Z","abstract_excerpt":"We study the dynamics of the Fisher-KPP equation on the infinite homogeneous tree and Erd\\H{o}s-R\\'eyni random graphs. We assume initial data that is zero everywhere except at a single node. For the case of the homogeneous tree, the solution will either form a traveling front or converge pointwise to zero. This dichotomy is determined by the linear spreading speed and we compute critical values of the diffusion parameter for which the spreading speed is zero and maximal and prove that the system is linearly determined. We also study the growth of the total population in the network and identif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06877","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.06877","created_at":"2026-05-18T00:16:56.756134+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.06877v3","created_at":"2026-05-18T00:16:56.756134+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06877","created_at":"2026-05-18T00:16:56.756134+00:00"},{"alias_kind":"pith_short_12","alias_value":"JQAUZSOAPZQM","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JQAUZSOAPZQMNKEV","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JQAUZSOA","created_at":"2026-05-18T12:30:25.849896+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JQAUZSOAPZQMNKEVF6PD2AA7LR","json":"https://pith.science/pith/JQAUZSOAPZQMNKEVF6PD2AA7LR.json","graph_json":"https://pith.science/api/pith-number/JQAUZSOAPZQMNKEVF6PD2AA7LR/graph.json","events_json":"https://pith.science/api/pith-number/JQAUZSOAPZQMNKEVF6PD2AA7LR/events.json","paper":"https://pith.science/paper/JQAUZSOA"},"agent_actions":{"view_html":"https://pith.science/pith/JQAUZSOAPZQMNKEVF6PD2AA7LR","download_json":"https://pith.science/pith/JQAUZSOAPZQMNKEVF6PD2AA7LR.json","view_paper":"https://pith.science/paper/JQAUZSOA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.06877&json=true","fetch_graph":"https://pith.science/api/pith-number/JQAUZSOAPZQMNKEVF6PD2AA7LR/graph.json","fetch_events":"https://pith.science/api/pith-number/JQAUZSOAPZQMNKEVF6PD2AA7LR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JQAUZSOAPZQMNKEVF6PD2AA7LR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JQAUZSOAPZQMNKEVF6PD2AA7LR/action/storage_attestation","attest_author":"https://pith.science/pith/JQAUZSOAPZQMNKEVF6PD2AA7LR/action/author_attestation","sign_citation":"https://pith.science/pith/JQAUZSOAPZQMNKEVF6PD2AA7LR/action/citation_signature","submit_replication":"https://pith.science/pith/JQAUZSOAPZQMNKEVF6PD2AA7LR/action/replication_record"}},"created_at":"2026-05-18T00:16:56.756134+00:00","updated_at":"2026-05-18T00:16:56.756134+00:00"}