Pith Number

pith:GAUQDE2V

pith:2012:GAUQDE2VQQV2DNIR2CL4E5QXCY

not attested not anchored not stored refs pending

Digital sum inequalities and approximate convexity of Takagi-type functions

Pieter C. Allaart

arxiv:1208.2745 v1 · 2012-08-14 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GAUQDE2VQQV2DNIR2CL4E5QXCY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-18T02:52:12.902177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3029019355842ba1b511d097c2761716335305a277cd12c42fb64f0df198f280

Aliases

arxiv: 1208.2745 · arxiv_version: 1208.2745v1 · doi: 10.48550/arxiv.1208.2745 · pith_short_12: GAUQDE2VQQV2 · pith_short_16: GAUQDE2VQQV2DNIR · pith_short_8: GAUQDE2V

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/GAUQDE2VQQV2DNIR2CL4E5QXCY \
  | 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: 3029019355842ba1b511d097c2761716335305a277cd12c42fb64f0df198f280

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e23c1437a94ef51fbf84e2bab91867b8657f063a67e0526508d0821c3cd7be33",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-14T01:24:58Z",
    "title_canon_sha256": "6e391a348275189b9abfc3f1a6525a3c108c592e8e660eafbe51a2591ef8c2c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2745",
    "kind": "arxiv",
    "version": 1
  }
}