Pith Number

pith:WMGWHT4P

pith:2026:WMGWHT4PTLMRBLSFCCRWO4SBKQ

not attested not anchored not stored refs pending

Values of algebraic functions at Liouville numbers

Diego Marques, Yuri Bilu

Algebraic functions of degree m map all L-numbers to U_m-numbers under general assumptions.

arxiv:2604.08818 v3 · 2026-04-09 · math.NT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WMGWHT4PTLMRBLSFCCRWO4SBKQ}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

under very general assumptions, an algebraic function of degree m takes U_m-values at all L-numbers.

C2weakest assumption

The 'very general assumptions' on the algebraic function u of degree m and the precise definition of the class of L-numbers are broad enough for the claimed statement to hold.

C3one line summary

Algebraic functions of degree m take U_m-values at all L-numbers under general assumptions.

Receipt and verification

First computed	2026-05-20T01:05:12.858267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b30d63cf8f9ad910ae4510a3677241543c74033f06c5de406545d84abb5a7b25

Aliases

arxiv: 2604.08818 · arxiv_version: 2604.08818v3 · doi: 10.48550/arxiv.2604.08818 · pith_short_12: WMGWHT4PTLMR · pith_short_16: WMGWHT4PTLMRBLSF · pith_short_8: WMGWHT4P

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WMGWHT4PTLMRBLSFCCRWO4SBKQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b30d63cf8f9ad910ae4510a3677241543c74033f06c5de406545d84abb5a7b25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f3edf0ce8085a102bbc8a198e65472ab0ef678c89a2c47959b95a7ef0fb5026",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-04-09T23:17:42Z",
    "title_canon_sha256": "5ee09937ff87eab49082a9f2c3f9dfaea55e0de9db470f218e35f1de3f3bcd6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.08818",
    "kind": "arxiv",
    "version": 3
  }
}