{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EEMUJ5KZR3DWVEN5VKDZHZUQ3Y","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":"5f9b3804b714677afa55ee5c5718a5db82377416b31e49e09eef9eeb70516f15","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-21T04:47:34Z","title_canon_sha256":"3979523a3beac1a320360bb7c5216bc9da9e45ce6f4cf9916c4f12f508091605"},"schema_version":"1.0","source":{"id":"1504.05303","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05303","created_at":"2026-05-18T02:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05303v2","created_at":"2026-05-18T02:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05303","created_at":"2026-05-18T02:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"EEMUJ5KZR3DW","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EEMUJ5KZR3DWVEN5","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EEMUJ5KZ","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:68bc7c5b1758c48933e0d9aff1dc2b73050481b0cece972abee2f5271afcb08b","target":"graph","created_at":"2026-05-18T02:17:54Z","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":"Multiple Landen values (MLVs) are defined as iterated integrals on the interval $x\\in[0,1]$ of the differential forms $A=d\\log(x)$, $B=-d\\log(1-x)$, $F=-d\\log(1-\\rho^2x)$ and $G=-d\\log(1-\\rho x)$, where $\\rho=(\\sqrt{5}-1)/2$ is the golden section. I conjecture that the dimension of the space of ${\\mathbb Z}$-linearly independent MLVs of weight $w$ is a tribonacci number $T_w$, generated by $1/(1-x-x^2- x^3)=1+\\sum_{w>0}T_w x^w$, and that a basis is provided by all the words in the $\\{A,G\\}$ sub-alphabet that neither end in $A$ nor contain $A^3$. For $w<9$, I construct a much more efficient bas","authors_text":"David Broadhurst","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-21T04:47:34Z","title":"Multiple Landen values and the tribonacci numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05303","kind":"arxiv","version":2},"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":"sha256:1f95022e09ccbefdc02f6c4537ceba551281de1a4e6ad96ec1728a67bccc12aa","target":"record","created_at":"2026-05-18T02:17:54Z","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":"5f9b3804b714677afa55ee5c5718a5db82377416b31e49e09eef9eeb70516f15","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-21T04:47:34Z","title_canon_sha256":"3979523a3beac1a320360bb7c5216bc9da9e45ce6f4cf9916c4f12f508091605"},"schema_version":"1.0","source":{"id":"1504.05303","kind":"arxiv","version":2}},"canonical_sha256":"211944f5598ec76a91bdaa8793e690de3bb47ef2270cd94384c96e7b7d269e19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"211944f5598ec76a91bdaa8793e690de3bb47ef2270cd94384c96e7b7d269e19","first_computed_at":"2026-05-18T02:17:54.017650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:54.017650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aOyRlECSHZBX4CL/pxIhP3fttK5cfPSj9UJhO/AR5YnId6ex0ikHYle1qF0why3m/ruqhyGvvmKdaamuV3jYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:54.018397Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05303","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f95022e09ccbefdc02f6c4537ceba551281de1a4e6ad96ec1728a67bccc12aa","sha256:68bc7c5b1758c48933e0d9aff1dc2b73050481b0cece972abee2f5271afcb08b"],"state_sha256":"7e6c23a40b342f0b0a41783c97bed83daf2116ff4d96c014b035395504d7071a"}