Pith Number

pith:6DE3VXJY

pith:2003:6DE3VXJYQBHIPA7MLH2PXGOZLI

not attested not anchored not stored refs pending

Some approximation theorems

N. V. Rao

arxiv:math/0312123 v1 · 2003-12-05 · math.FA · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6DE3VXJYQBHIPA7MLH2PXGOZLI}

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	2026-05-18T01:05:26.691216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0c9badd38804e8783ec59f4fb99d95a2afae1065ce4345575835f31ea95ca1b

Aliases

arxiv: math/0312123 · arxiv_version: math/0312123v1 · doi: 10.48550/arxiv.math/0312123 · pith_short_12: 6DE3VXJYQBHI · pith_short_16: 6DE3VXJYQBHIPA7M · pith_short_8: 6DE3VXJY

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/6DE3VXJYQBHIPA7MLH2PXGOZLI \
  | 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: f0c9badd38804e8783ec59f4fb99d95a2afae1065ce4345575835f31ea95ca1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbba6793364444ec430ab0cf4d1daeb47664c3b52608a0dc9701a8b5707ceaa6",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2003-12-05T10:55:48Z",
    "title_canon_sha256": "dbfc3e9f05e9948216e260e92f0e3782d8ba63595a941d5f335118da5eada966"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0312123",
    "kind": "arxiv",
    "version": 1
  }
}