{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:R4X7POVZEPM2BPIZ72YTBUH3B2","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":"4178cd428a164a450e17fc58f331d484025c4c108adaf6aa70eab06e3a2f023e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-05T11:35:38Z","title_canon_sha256":"baddef01c6184b477c59d24b6d3113522f84e9bafdb69cc4a83453ea29beacb7"},"schema_version":"1.0","source":{"id":"1610.01369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01369","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01369v1","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01369","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"R4X7POVZEPM2","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R4X7POVZEPM2BPIZ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R4X7POVZ","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:3aa129bc535f07c712cf809e6e21a2322c8f43b5a734b4f42f2ee78f107c78a0","target":"graph","created_at":"2026-05-18T01:03:11Z","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 introduce the concept of fractels for functions and discuss their analytic and algebraic properties. We also consider the representation of polynomials and analytic functions using fractels, and the consequences of these representations in numerical analysis.","authors_text":"Markus Hegland, Michael Barnsley, Peter Massopust","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-05T11:35:38Z","title":"Self-referential Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01369","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:e2e842f71be90e6fdbdfa92e0bdc8d2a27853acb9c48561df97c6c11727d0ac3","target":"record","created_at":"2026-05-18T01:03:11Z","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":"4178cd428a164a450e17fc58f331d484025c4c108adaf6aa70eab06e3a2f023e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-05T11:35:38Z","title_canon_sha256":"baddef01c6184b477c59d24b6d3113522f84e9bafdb69cc4a83453ea29beacb7"},"schema_version":"1.0","source":{"id":"1610.01369","kind":"arxiv","version":1}},"canonical_sha256":"8f2ff7bab923d9a0bd19feb130d0fb0e898b23c36f95ff3be5fb7aaf1c0026d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f2ff7bab923d9a0bd19feb130d0fb0e898b23c36f95ff3be5fb7aaf1c0026d0","first_computed_at":"2026-05-18T01:03:11.019256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:11.019256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n6Pj4ZaIRX2KwFI/7tQNxBvNOXphU/qDXcZQF6tdB4H5Pk1FowOacOoWVfDGxbZw17j6DyrnFqH0qMPUa/58Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:11.019683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2e842f71be90e6fdbdfa92e0bdc8d2a27853acb9c48561df97c6c11727d0ac3","sha256:3aa129bc535f07c712cf809e6e21a2322c8f43b5a734b4f42f2ee78f107c78a0"],"state_sha256":"45d656e74e8c56e0329ce16e401d2b2f5f2b7c65f89a327268bb66830834d710"}