{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JOKQTOUSUYAZFUBHR5COLVXTTR","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":"2ae1e00670918ec87457f473dc966f14fe22eaf2c7037a5e075b34b913d4b01c","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-09T10:42:45Z","title_canon_sha256":"f095fc39389b82bcf5ec569a3902432fd9ae4ef27d95657355373aa660eef062"},"schema_version":"1.0","source":{"id":"2506.07625","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07625","created_at":"2026-07-05T12:04:15Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07625v6","created_at":"2026-07-05T12:04:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07625","created_at":"2026-07-05T12:04:15Z"},{"alias_kind":"pith_short_12","alias_value":"JOKQTOUSUYAZ","created_at":"2026-07-05T12:04:15Z"},{"alias_kind":"pith_short_16","alias_value":"JOKQTOUSUYAZFUBH","created_at":"2026-07-05T12:04:15Z"},{"alias_kind":"pith_short_8","alias_value":"JOKQTOUS","created_at":"2026-07-05T12:04:15Z"}],"graph_snapshots":[{"event_id":"sha256:0ae640b6679ca8daa1e29ad5e2d90c0d7f91ecc237deebfda9ec8bfe3e6137bc","target":"graph","created_at":"2026-07-05T12:04:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.07625/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The vivid contrast between two competing algorithms for solving Abel's equation $g(\\theta(x)) = g(x) + 1$, given $\\theta(x)$, is easily sketched. EJ is faster and more efficient, but ML evaluates a limit characterizing the principal solution $g(x)$ directly. EJ finds $g(x)+\\delta$, where $\\delta$ is possibly nonzero but independent of $x$. If we were to know an exact expression for $\\delta$, then the \"intrinsicality\" of ML would be subsumed by EJ. Filling this gap in our knowledge is the aim of this paper.","authors_text":"Steven Finch","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-09T10:42:45Z","title":"Half-Iterates and Delta Conjectures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07625","kind":"arxiv","version":6},"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":"sha256:245b131027c6ada38fe1735c8c4688e51f8770a3470ac1dafc978727f3498cce","target":"record","created_at":"2026-07-05T12:04:15Z","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":"2ae1e00670918ec87457f473dc966f14fe22eaf2c7037a5e075b34b913d4b01c","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-09T10:42:45Z","title_canon_sha256":"f095fc39389b82bcf5ec569a3902432fd9ae4ef27d95657355373aa660eef062"},"schema_version":"1.0","source":{"id":"2506.07625","kind":"arxiv","version":6}},"canonical_sha256":"4b9509ba92a60192d0278f44e5d6f39c4560ef6516e2ce1ef0702494d027c76f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b9509ba92a60192d0278f44e5d6f39c4560ef6516e2ce1ef0702494d027c76f","first_computed_at":"2026-07-05T12:04:15.537790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:04:15.537790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bss8UY98KzpwYbbfVMfFS3d/G3xlEjF6xsXmeUGyJYt+31WZs2DxiPfX6zlm/BHSpp3M8BM0/XXyzCS8Hva/AA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:04:15.538401Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07625","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:245b131027c6ada38fe1735c8c4688e51f8770a3470ac1dafc978727f3498cce","sha256:0ae640b6679ca8daa1e29ad5e2d90c0d7f91ecc237deebfda9ec8bfe3e6137bc"],"state_sha256":"aee8a3c8bcbaa701e79ed64fb5117dfaf3db6137829f110021e99ec420525c31"}