Pith Number

pith:VXT2TMSQ

pith:2012:VXT2TMSQ2WGCPUOCIFBC7VSUTB

not attested not anchored not stored refs pending

On $C^{0}$-fine approximation of convex functions by real analytic convex functions

Daniel Azagra

arxiv:1201.3858 v2 · 2012-01-18 · math.CA · math.DG · 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{VXT2TMSQ2WGCPUOCIFBC7VSUTB}

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	2026-05-18T04:04:06.220192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ade7a9b250d58c27d1c241422fd654984dfadcf277780fccfdf153302c9aad2d

Aliases

arxiv: 1201.3858 · arxiv_version: 1201.3858v2 · doi: 10.48550/arxiv.1201.3858 · pith_short_12: VXT2TMSQ2WGC · pith_short_16: VXT2TMSQ2WGCPUOC · pith_short_8: VXT2TMSQ

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/VXT2TMSQ2WGCPUOCIFBC7VSUTB \
  | 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: ade7a9b250d58c27d1c241422fd654984dfadcf277780fccfdf153302c9aad2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50599dbfbd9866f4cf831e7e585d62c9ba3e18b83884417a936f7b637e25a0dd",
    "cross_cats_sorted": [
      "math.DG",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-01-18T17:18:40Z",
    "title_canon_sha256": "de6ddc3033999da0adead8d1803cec997aa18b4515617de6951c350aa6bb0569"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3858",
    "kind": "arxiv",
    "version": 2
  }
}