{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WEMGIFFGDLVWQBDZ2UJVX6GHCR","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":"dcc7b4b5be76ec8b180563a98b614978eb3eed4eceea1d215394063674642de0","cross_cats_sorted":["hep-th","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-27T11:13:15Z","title_canon_sha256":"81fbbff86e205d204220ce4b8a2be90e6b9f7bcd7f7e7164c80c7ef9fda1bc94"},"schema_version":"1.0","source":{"id":"1005.5030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5030","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5030v1","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5030","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"WEMGIFFGDLVW","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WEMGIFFGDLVWQBDZ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WEMGIFFG","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:0c48f9dcfe9d78aaf65d060efd356c4a0bc9ce336d0e69198ab3f1d618ff6c24","target":"graph","created_at":"2026-05-18T04:31:41Z","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":"We develop and illustrate methods to compute all single particle potentials that underlie the logistic map, x --> sx(1-x) for 0<s<=4. We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the various branches of the corresponding analytic potential functions, which have an infinite number of branch points for generic s>2. We illustrate the methods numerically for the cases s=5/2 and s=10/3.","authors_text":"Andrzej Veitia, Thomas Curtright","cross_cats":["hep-th","math.MP","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-27T11:13:15Z","title":"Logistic Map Potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5030","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":"sha256:8f1fc5bce64f4808c637fdd3e457e63c59ba64de327252c437230aa66e82f6c3","target":"record","created_at":"2026-05-18T04:31:41Z","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":"dcc7b4b5be76ec8b180563a98b614978eb3eed4eceea1d215394063674642de0","cross_cats_sorted":["hep-th","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-27T11:13:15Z","title_canon_sha256":"81fbbff86e205d204220ce4b8a2be90e6b9f7bcd7f7e7164c80c7ef9fda1bc94"},"schema_version":"1.0","source":{"id":"1005.5030","kind":"arxiv","version":1}},"canonical_sha256":"b1186414a61aeb680479d5135bf8c71452d48dde074e2aebd468e62bdc067505","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1186414a61aeb680479d5135bf8c71452d48dde074e2aebd468e62bdc067505","first_computed_at":"2026-05-18T04:31:41.152699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:41.152699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R6Ht1/ZP5iwJfGdCnIFcnWZ46iSt/X30MZN13Q0O6dYCewknomrsaGSYFMpFG4Xv+V/wsrcOq19RdCSaK+0KCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:41.153407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.5030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f1fc5bce64f4808c637fdd3e457e63c59ba64de327252c437230aa66e82f6c3","sha256:0c48f9dcfe9d78aaf65d060efd356c4a0bc9ce336d0e69198ab3f1d618ff6c24"],"state_sha256":"83cd99b225fca4ade99d0a71fd00dac98425f0199940fc5805873b3ed47202c6"}