Pith Number

pith:M4332PYE

pith:2012:M4332PYEE3JD6ATZULQ5APAVWY

not attested not anchored not stored refs pending

Global and fine approximation of convex functions

Daniel Azagra

arxiv:1201.4760 v6 · 2012-01-23 · math.DG · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M4332PYEE3JD6ATZULQ5APAVWY}

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	2026-05-18T02:39:32.426886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6737bd3f0426d23f0279a2e1d03c15b636f4407094a011818bed096deccffd22

Aliases

arxiv: 1201.4760 · arxiv_version: 1201.4760v6 · doi: 10.48550/arxiv.1201.4760 · pith_short_12: M4332PYEE3JD · pith_short_16: M4332PYEE3JD6ATZ · pith_short_8: M4332PYE

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/M4332PYEE3JD6ATZULQ5APAVWY \
  | 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: 6737bd3f0426d23f0279a2e1d03c15b636f4407094a011818bed096deccffd22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "245b4a6f03664bc4f5140b2267c74288a43697f99535250341f2ab91a9062e95",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-01-23T16:40:56Z",
    "title_canon_sha256": "099734eb2b98b29e518350b4f26feb93e805d2f6b48aa4bfd1fb44131fac0cfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4760",
    "kind": "arxiv",
    "version": 6
  }
}