{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5RTFYPXP5Q2CM6KAUU4RJ5L2O7","short_pith_number":"pith:5RTFYPXP","schema_version":"1.0","canonical_sha256":"ec665c3eefec34267940a53914f57a77f00564e7c0ebb379565bad537b991c7b","source":{"kind":"arxiv","id":"2607.16088","version":1},"attestation_state":"computed","paper":{"title":"A Variable-Length Gray Code for the Natural Numbers","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ezequiel L\\'opez-Rubio","submitted_at":"2026-07-17T16:18:40Z","abstract_excerpt":"The reflected binary Gray code arranges the fixed-length binary representations of the integers so that consecutive numbers differ in a single bit. Its usefulness, however, is tied to a fixed word length $b$, which both caps the range of representable numbers at $2^{b}-1$ and wastes bits on small integers. We introduce a \\emph{variable-length Gray code} $\\V$, a total function from the natural numbers to the set of all finite binary strings, obtained by taking the reflected Gray code of $n+1$, discarding its leading zeros, and deleting the single leading one. We prove four properties of this co"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.16088","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-07-17T16:18:40Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6da3bd560979ac4b960f8dad8a2a6e34115d875c4f429216b56a55a8d60cc525","abstract_canon_sha256":"39550fb894f6fc39cb6d721904867db3a8a333aa1b1a16a79c8e73c63553e122"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-20T02:19:30.297255Z","signature_b64":"C36R2G38QNF2q73K9/dH/ynDOM3b2GuCnVHbddNymoK4YpWlfVU+gkR1VTZsMLthNy0GoJQ9XFlzNp3ylb1VDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec665c3eefec34267940a53914f57a77f00564e7c0ebb379565bad537b991c7b","last_reissued_at":"2026-07-20T02:19:30.296443Z","signature_status":"signed_v1","first_computed_at":"2026-07-20T02:19:30.296443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Variable-Length Gray Code for the Natural Numbers","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ezequiel L\\'opez-Rubio","submitted_at":"2026-07-17T16:18:40Z","abstract_excerpt":"The reflected binary Gray code arranges the fixed-length binary representations of the integers so that consecutive numbers differ in a single bit. Its usefulness, however, is tied to a fixed word length $b$, which both caps the range of representable numbers at $2^{b}-1$ and wastes bits on small integers. We introduce a \\emph{variable-length Gray code} $\\V$, a total function from the natural numbers to the set of all finite binary strings, obtained by taking the reflected Gray code of $n+1$, discarding its leading zeros, and deleting the single leading one. We prove four properties of this co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16088","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16088/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.16088","created_at":"2026-07-20T02:19:30.296856+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.16088v1","created_at":"2026-07-20T02:19:30.296856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16088","created_at":"2026-07-20T02:19:30.296856+00:00"},{"alias_kind":"pith_short_12","alias_value":"5RTFYPXP5Q2C","created_at":"2026-07-20T02:19:30.296856+00:00"},{"alias_kind":"pith_short_16","alias_value":"5RTFYPXP5Q2CM6KA","created_at":"2026-07-20T02:19:30.296856+00:00"},{"alias_kind":"pith_short_8","alias_value":"5RTFYPXP","created_at":"2026-07-20T02:19:30.296856+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5RTFYPXP5Q2CM6KAUU4RJ5L2O7","json":"https://pith.science/pith/5RTFYPXP5Q2CM6KAUU4RJ5L2O7.json","graph_json":"https://pith.science/api/pith-number/5RTFYPXP5Q2CM6KAUU4RJ5L2O7/graph.json","events_json":"https://pith.science/api/pith-number/5RTFYPXP5Q2CM6KAUU4RJ5L2O7/events.json","paper":"https://pith.science/paper/5RTFYPXP"},"agent_actions":{"view_html":"https://pith.science/pith/5RTFYPXP5Q2CM6KAUU4RJ5L2O7","download_json":"https://pith.science/pith/5RTFYPXP5Q2CM6KAUU4RJ5L2O7.json","view_paper":"https://pith.science/paper/5RTFYPXP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.16088&json=true","fetch_graph":"https://pith.science/api/pith-number/5RTFYPXP5Q2CM6KAUU4RJ5L2O7/graph.json","fetch_events":"https://pith.science/api/pith-number/5RTFYPXP5Q2CM6KAUU4RJ5L2O7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5RTFYPXP5Q2CM6KAUU4RJ5L2O7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5RTFYPXP5Q2CM6KAUU4RJ5L2O7/action/storage_attestation","attest_author":"https://pith.science/pith/5RTFYPXP5Q2CM6KAUU4RJ5L2O7/action/author_attestation","sign_citation":"https://pith.science/pith/5RTFYPXP5Q2CM6KAUU4RJ5L2O7/action/citation_signature","submit_replication":"https://pith.science/pith/5RTFYPXP5Q2CM6KAUU4RJ5L2O7/action/replication_record"}},"created_at":"2026-07-20T02:19:30.296856+00:00","updated_at":"2026-07-20T02:19:30.296856+00:00"}