{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7RDBEAYOUZ5AIWIPD5TXPZCI7W","short_pith_number":"pith:7RDBEAYO","canonical_record":{"source":{"id":"1804.07628","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-04-20T14:12:51Z","cross_cats_sorted":[],"title_canon_sha256":"5f630a80e82a1ed6f758dc987bb64a07934ee7f1f7a11197198d16b0f3d87f7e","abstract_canon_sha256":"a61f142fdb17b962104d7d3c2dd8c7e2c829190108c02b288c530f52b3bb35f2"},"schema_version":"1.0"},"canonical_sha256":"fc4612030ea67a04590f1f6777e448fd81efd5fe3da41b7c8a238f15c9fed337","source":{"kind":"arxiv","id":"1804.07628","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07628","created_at":"2026-05-17T23:45:38Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07628v3","created_at":"2026-05-17T23:45:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07628","created_at":"2026-05-17T23:45:38Z"},{"alias_kind":"pith_short_12","alias_value":"7RDBEAYOUZ5A","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7RDBEAYOUZ5AIWIP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7RDBEAYO","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7RDBEAYOUZ5AIWIPD5TXPZCI7W","target":"record","payload":{"canonical_record":{"source":{"id":"1804.07628","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-04-20T14:12:51Z","cross_cats_sorted":[],"title_canon_sha256":"5f630a80e82a1ed6f758dc987bb64a07934ee7f1f7a11197198d16b0f3d87f7e","abstract_canon_sha256":"a61f142fdb17b962104d7d3c2dd8c7e2c829190108c02b288c530f52b3bb35f2"},"schema_version":"1.0"},"canonical_sha256":"fc4612030ea67a04590f1f6777e448fd81efd5fe3da41b7c8a238f15c9fed337","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:38.628722Z","signature_b64":"F8/9nxJnzxQV0/vhDFghL24QdY0UVXCeqP5OPfU0p0JHFZNeSg5nH8KatHbAgQ/HYPHZiVzxyRaCbzZJ3ZZ4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc4612030ea67a04590f1f6777e448fd81efd5fe3da41b7c8a238f15c9fed337","last_reissued_at":"2026-05-17T23:45:38.628136Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:38.628136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.07628","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jtqE4B9kOORNRR3vQiMOmI4rh2d4SP/lpLcLJNxzwWEjf8b4q2BChEyM19zugzpjpJv5cpKZWXr1rNiONcyJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:31:04.673329Z"},"content_sha256":"03c4901ff2a9861a922e467906d6108e396627f9f40ce96400405108d0281c12","schema_version":"1.0","event_id":"sha256:03c4901ff2a9861a922e467906d6108e396627f9f40ce96400405108d0281c12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7RDBEAYOUZ5AIWIPD5TXPZCI7W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localized solutions of nonlinear network wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"A. B. Aceves, A. Knippel, I. Khames, J. G. Caputo","submitted_at":"2018-04-20T14:12:51Z","abstract_excerpt":"We study localized solutions for the nonlinear graph wave equation on finite arbitrary networks. Assuming a large amplitude localized initial condition on one node of the graph, we approximate its evolution by the Duffing equation. The rest of the network satisfies a linear system forced by the excited node. This approximation is validated by reducing the nonlinear graph wave equation to the discrete nonlinear Schrodinger equation and by Fourier analysis. Finally, we examine numerically the condition for localization in the parameter plane, coupling versus amplitude and show that the localizat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07628","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"deoC3MIQ0+tQf4oU+pb/KipFFxUImYDVEL8coh7k0lmcCSTnc10wHFBYfK9pQcJxJSLzp311pvDfVEkB7tLcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:31:04.673987Z"},"content_sha256":"45a0e7208fcedf54719bcf6418ed685088bd755c353c22312941651f78ce92c1","schema_version":"1.0","event_id":"sha256:45a0e7208fcedf54719bcf6418ed685088bd755c353c22312941651f78ce92c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RDBEAYOUZ5AIWIPD5TXPZCI7W/bundle.json","state_url":"https://pith.science/pith/7RDBEAYOUZ5AIWIPD5TXPZCI7W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RDBEAYOUZ5AIWIPD5TXPZCI7W/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":"2026-06-07T18:31:04Z","links":{"resolver":"https://pith.science/pith/7RDBEAYOUZ5AIWIPD5TXPZCI7W","bundle":"https://pith.science/pith/7RDBEAYOUZ5AIWIPD5TXPZCI7W/bundle.json","state":"https://pith.science/pith/7RDBEAYOUZ5AIWIPD5TXPZCI7W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RDBEAYOUZ5AIWIPD5TXPZCI7W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7RDBEAYOUZ5AIWIPD5TXPZCI7W","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":"a61f142fdb17b962104d7d3c2dd8c7e2c829190108c02b288c530f52b3bb35f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-04-20T14:12:51Z","title_canon_sha256":"5f630a80e82a1ed6f758dc987bb64a07934ee7f1f7a11197198d16b0f3d87f7e"},"schema_version":"1.0","source":{"id":"1804.07628","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07628","created_at":"2026-05-17T23:45:38Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07628v3","created_at":"2026-05-17T23:45:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07628","created_at":"2026-05-17T23:45:38Z"},{"alias_kind":"pith_short_12","alias_value":"7RDBEAYOUZ5A","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7RDBEAYOUZ5AIWIP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7RDBEAYO","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:45a0e7208fcedf54719bcf6418ed685088bd755c353c22312941651f78ce92c1","target":"graph","created_at":"2026-05-17T23:45:38Z","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 study localized solutions for the nonlinear graph wave equation on finite arbitrary networks. Assuming a large amplitude localized initial condition on one node of the graph, we approximate its evolution by the Duffing equation. The rest of the network satisfies a linear system forced by the excited node. This approximation is validated by reducing the nonlinear graph wave equation to the discrete nonlinear Schrodinger equation and by Fourier analysis. Finally, we examine numerically the condition for localization in the parameter plane, coupling versus amplitude and show that the localizat","authors_text":"A. B. Aceves, A. Knippel, I. Khames, J. G. Caputo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-04-20T14:12:51Z","title":"Localized solutions of nonlinear network wave equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07628","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":"sha256:03c4901ff2a9861a922e467906d6108e396627f9f40ce96400405108d0281c12","target":"record","created_at":"2026-05-17T23:45:38Z","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":"a61f142fdb17b962104d7d3c2dd8c7e2c829190108c02b288c530f52b3bb35f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-04-20T14:12:51Z","title_canon_sha256":"5f630a80e82a1ed6f758dc987bb64a07934ee7f1f7a11197198d16b0f3d87f7e"},"schema_version":"1.0","source":{"id":"1804.07628","kind":"arxiv","version":3}},"canonical_sha256":"fc4612030ea67a04590f1f6777e448fd81efd5fe3da41b7c8a238f15c9fed337","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc4612030ea67a04590f1f6777e448fd81efd5fe3da41b7c8a238f15c9fed337","first_computed_at":"2026-05-17T23:45:38.628136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:38.628136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F8/9nxJnzxQV0/vhDFghL24QdY0UVXCeqP5OPfU0p0JHFZNeSg5nH8KatHbAgQ/HYPHZiVzxyRaCbzZJ3ZZ4BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:38.628722Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07628","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03c4901ff2a9861a922e467906d6108e396627f9f40ce96400405108d0281c12","sha256:45a0e7208fcedf54719bcf6418ed685088bd755c353c22312941651f78ce92c1"],"state_sha256":"d2089bf2472fbfcc89c8bd3a2c25134fc41f229a37f6d4a889a72975d6b7aac5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNGiorhTKo5zZEAuYDuKhssDAQP8BKu0cQIPQ7GOdHZPdDVqZ08yLdK/HvYAjIKgR9HNJdaKA2hPIy4hqi9yCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:31:04.677597Z","bundle_sha256":"dbe73fcaae09f4bae7ce4a3556df9333705cab32f7c6da9d2c72577df0f30bd0"}}