{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:R4X7POVZEPM2BPIZ72YTBUH3B2","short_pith_number":"pith:R4X7POVZ","canonical_record":{"source":{"id":"1610.01369","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-05T11:35:38Z","cross_cats_sorted":[],"title_canon_sha256":"baddef01c6184b477c59d24b6d3113522f84e9bafdb69cc4a83453ea29beacb7","abstract_canon_sha256":"4178cd428a164a450e17fc58f331d484025c4c108adaf6aa70eab06e3a2f023e"},"schema_version":"1.0"},"canonical_sha256":"8f2ff7bab923d9a0bd19feb130d0fb0e898b23c36f95ff3be5fb7aaf1c0026d0","source":{"kind":"arxiv","id":"1610.01369","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:R4X7POVZEPM2BPIZ72YTBUH3B2","target":"record","payload":{"canonical_record":{"source":{"id":"1610.01369","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-05T11:35:38Z","cross_cats_sorted":[],"title_canon_sha256":"baddef01c6184b477c59d24b6d3113522f84e9bafdb69cc4a83453ea29beacb7","abstract_canon_sha256":"4178cd428a164a450e17fc58f331d484025c4c108adaf6aa70eab06e3a2f023e"},"schema_version":"1.0"},"canonical_sha256":"8f2ff7bab923d9a0bd19feb130d0fb0e898b23c36f95ff3be5fb7aaf1c0026d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:11.019683Z","signature_b64":"n6Pj4ZaIRX2KwFI/7tQNxBvNOXphU/qDXcZQF6tdB4H5Pk1FowOacOoWVfDGxbZw17j6DyrnFqH0qMPUa/58Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f2ff7bab923d9a0bd19feb130d0fb0e898b23c36f95ff3be5fb7aaf1c0026d0","last_reissued_at":"2026-05-18T01:03:11.019256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:11.019256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.01369","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9YeNvxREiMMnY83kqg6agFrb4juc+JSf+fiyTbdbJHPC4U25wh/afF5Sr0IKxHKSGJHshuAwHOyrWWjXmyD/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:34:06.914102Z"},"content_sha256":"e2e842f71be90e6fdbdfa92e0bdc8d2a27853acb9c48561df97c6c11727d0ac3","schema_version":"1.0","event_id":"sha256:e2e842f71be90e6fdbdfa92e0bdc8d2a27853acb9c48561df97c6c11727d0ac3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:R4X7POVZEPM2BPIZ72YTBUH3B2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-referential Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Markus Hegland, Michael Barnsley, Peter Massopust","submitted_at":"2016-10-05T11:35:38Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01369","kind":"arxiv","version":1},"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":"2026-05-18T01:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZfIawnyk98c3R6M/QYjzATiNdOSJeps4zrrsv5CHO25Bet9ZhZwGAIxMIp+9HJ56itnhgSOED1+tiRP+NLFHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:34:06.914455Z"},"content_sha256":"3aa129bc535f07c712cf809e6e21a2322c8f43b5a734b4f42f2ee78f107c78a0","schema_version":"1.0","event_id":"sha256:3aa129bc535f07c712cf809e6e21a2322c8f43b5a734b4f42f2ee78f107c78a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4X7POVZEPM2BPIZ72YTBUH3B2/bundle.json","state_url":"https://pith.science/pith/R4X7POVZEPM2BPIZ72YTBUH3B2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4X7POVZEPM2BPIZ72YTBUH3B2/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":"2026-06-08T22:34:06Z","links":{"resolver":"https://pith.science/pith/R4X7POVZEPM2BPIZ72YTBUH3B2","bundle":"https://pith.science/pith/R4X7POVZEPM2BPIZ72YTBUH3B2/bundle.json","state":"https://pith.science/pith/R4X7POVZEPM2BPIZ72YTBUH3B2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4X7POVZEPM2BPIZ72YTBUH3B2/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gNh+rhbL+OroRiyW/0Sh4tODj2KNnSNszqKSxcHTPvuMrJZvqLc17vRZYfTerKDUFRTjKgY8ktp3gpBgxUK6AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:34:06.916352Z","bundle_sha256":"616aae6e81408b0ec19646fe0e60cb434b785000ef24b1e7b785427e9031be32"}}