{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7SN6H3TLYCJUQD2A64GURQOVKN","short_pith_number":"pith:7SN6H3TL","canonical_record":{"source":{"id":"1409.0482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-01T17:11:07Z","cross_cats_sorted":[],"title_canon_sha256":"8acb3f6c19596fb9f2fac7c70354a88ef872e224f1aff5414f908508b4b2a66b","abstract_canon_sha256":"a89895dd42ab1568efc1161840228627821f315d8b9c889c1467eb8b23e421e7"},"schema_version":"1.0"},"canonical_sha256":"fc9be3ee6bc093480f40f70d48c1d55365efa08d4425bb6811981b1634bbef54","source":{"kind":"arxiv","id":"1409.0482","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0482","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0482v1","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0482","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"pith_short_12","alias_value":"7SN6H3TLYCJU","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7SN6H3TLYCJUQD2A","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7SN6H3TL","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7SN6H3TLYCJUQD2A64GURQOVKN","target":"record","payload":{"canonical_record":{"source":{"id":"1409.0482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-01T17:11:07Z","cross_cats_sorted":[],"title_canon_sha256":"8acb3f6c19596fb9f2fac7c70354a88ef872e224f1aff5414f908508b4b2a66b","abstract_canon_sha256":"a89895dd42ab1568efc1161840228627821f315d8b9c889c1467eb8b23e421e7"},"schema_version":"1.0"},"canonical_sha256":"fc9be3ee6bc093480f40f70d48c1d55365efa08d4425bb6811981b1634bbef54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:52.687478Z","signature_b64":"i0KF+VhpSv/W1pUBIIsLVzZ9i0D5kOjgCBwtdY7H5CC7hn5D4jByWQ0I9KwdR2INt9r2TEjdsUIj2zXYNZeYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc9be3ee6bc093480f40f70d48c1d55365efa08d4425bb6811981b1634bbef54","last_reissued_at":"2026-05-18T02:43:52.687053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:52.687053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.0482","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":"2026-05-18T02:43:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xksCOCK5fnouAhiO62ItkXhYfhlMHKhLm3H4e4u3hG87d8/LKmuZKF+uK0oAIevISDzjSYhV9LauE3+JI46+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:33:24.145162Z"},"content_sha256":"3af910b797c11d6626cbf79603974b769af44ed5b2ee14c0ab04717ab9a342f6","schema_version":"1.0","event_id":"sha256:3af910b797c11d6626cbf79603974b769af44ed5b2ee14c0ab04717ab9a342f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7SN6H3TLYCJUQD2A64GURQOVKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Benford Behavior of Zeckendorf Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew Best, Brian McDonald, Caroline Turnage-Butterbaugh, K. Tor, Madeleine Weinstein, Patrick Dynes, Steven J. Miller, Xixi Edelsbrunner","submitted_at":"2014-09-01T17:11:07Z","abstract_excerpt":"A beautiful theorem of Zeckendorf states that every integer can be written uniquely as the sum of non-consecutive Fibonacci numbers $\\{ F_i \\}_{i = 1}^{\\infty}$. A set $S \\subset \\mathbb{Z}$ is said to satisfy Benford's law if the density of the elements in $S$ with leading digit $d$ is $\\log_{10}{(1+\\frac{1}{d})}$; in other words, smaller leading digits are more likely to occur. We prove that, as $n\\to\\infty$, for a randomly selected integer $m$ in $[0, F_{n+1})$ the distribution of the leading digits of the Fibonacci summands in its Zeckendorf decomposition converge to Benford's law almost s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0482","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":"2026-05-18T02:43:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r+N5FwupIxU8PFTitCAU8gZkv0OWH88uTwH0QrfnZURjvweZvF3fF0dcXffmamniAo4iGMu/yS1UWPiGOPfNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:33:24.145533Z"},"content_sha256":"e959242dff31986107ce659aa9e9633f7ead7a3190c876346e56bffc8677478e","schema_version":"1.0","event_id":"sha256:e959242dff31986107ce659aa9e9633f7ead7a3190c876346e56bffc8677478e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SN6H3TLYCJUQD2A64GURQOVKN/bundle.json","state_url":"https://pith.science/pith/7SN6H3TLYCJUQD2A64GURQOVKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SN6H3TLYCJUQD2A64GURQOVKN/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":"2026-06-21T14:33:24Z","links":{"resolver":"https://pith.science/pith/7SN6H3TLYCJUQD2A64GURQOVKN","bundle":"https://pith.science/pith/7SN6H3TLYCJUQD2A64GURQOVKN/bundle.json","state":"https://pith.science/pith/7SN6H3TLYCJUQD2A64GURQOVKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SN6H3TLYCJUQD2A64GURQOVKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7SN6H3TLYCJUQD2A64GURQOVKN","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":"a89895dd42ab1568efc1161840228627821f315d8b9c889c1467eb8b23e421e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-01T17:11:07Z","title_canon_sha256":"8acb3f6c19596fb9f2fac7c70354a88ef872e224f1aff5414f908508b4b2a66b"},"schema_version":"1.0","source":{"id":"1409.0482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0482","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0482v1","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0482","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"pith_short_12","alias_value":"7SN6H3TLYCJU","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7SN6H3TLYCJUQD2A","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7SN6H3TL","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:e959242dff31986107ce659aa9e9633f7ead7a3190c876346e56bffc8677478e","target":"graph","created_at":"2026-05-18T02:43:52Z","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":"A beautiful theorem of Zeckendorf states that every integer can be written uniquely as the sum of non-consecutive Fibonacci numbers $\\{ F_i \\}_{i = 1}^{\\infty}$. A set $S \\subset \\mathbb{Z}$ is said to satisfy Benford's law if the density of the elements in $S$ with leading digit $d$ is $\\log_{10}{(1+\\frac{1}{d})}$; in other words, smaller leading digits are more likely to occur. We prove that, as $n\\to\\infty$, for a randomly selected integer $m$ in $[0, F_{n+1})$ the distribution of the leading digits of the Fibonacci summands in its Zeckendorf decomposition converge to Benford's law almost s","authors_text":"Andrew Best, Brian McDonald, Caroline Turnage-Butterbaugh, K. Tor, Madeleine Weinstein, Patrick Dynes, Steven J. Miller, Xixi Edelsbrunner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-01T17:11:07Z","title":"Benford Behavior of Zeckendorf Decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0482","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":"sha256:3af910b797c11d6626cbf79603974b769af44ed5b2ee14c0ab04717ab9a342f6","target":"record","created_at":"2026-05-18T02:43:52Z","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":"a89895dd42ab1568efc1161840228627821f315d8b9c889c1467eb8b23e421e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-01T17:11:07Z","title_canon_sha256":"8acb3f6c19596fb9f2fac7c70354a88ef872e224f1aff5414f908508b4b2a66b"},"schema_version":"1.0","source":{"id":"1409.0482","kind":"arxiv","version":1}},"canonical_sha256":"fc9be3ee6bc093480f40f70d48c1d55365efa08d4425bb6811981b1634bbef54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc9be3ee6bc093480f40f70d48c1d55365efa08d4425bb6811981b1634bbef54","first_computed_at":"2026-05-18T02:43:52.687053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:52.687053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i0KF+VhpSv/W1pUBIIsLVzZ9i0D5kOjgCBwtdY7H5CC7hn5D4jByWQ0I9KwdR2INt9r2TEjdsUIj2zXYNZeYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:52.687478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3af910b797c11d6626cbf79603974b769af44ed5b2ee14c0ab04717ab9a342f6","sha256:e959242dff31986107ce659aa9e9633f7ead7a3190c876346e56bffc8677478e"],"state_sha256":"22e871de586cf8e61b893ee86f0cd903da2f655f06f800db79d6394592bb524b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xt70oiY2EULjE+8EFegcjfgQftEIjWdUFF8R7/pMmshh5xEfsfnDi5lYhCkvtQrn3liEH1QQqPa75AuAKhrfAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T14:33:24.147470Z","bundle_sha256":"bc6619ab0e493b67e8d273c22be6152e8db8bbe961a0de470c933799db03e76a"}}