Pith Number

pith:HQFAVS72

pith:2009:HQFAVS72I2LNHGOWMQG5ROGE7D

not attested not anchored not stored refs pending

An extension of Alexandrov's theorem on second derivatives of convex functions

Joseph H.G. Fu

arxiv:0908.0278 v3 · 2009-08-03 · 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{HQFAVS72I2LNHGOWMQG5ROGE7D}

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	2026-05-18T03:26:00.452301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c0a0acbfa4696d399d6640dd8b8c4f8c8491f781af044f8d28ef0c33e9732a1

Aliases

arxiv: 0908.0278 · arxiv_version: 0908.0278v3 · doi: 10.48550/arxiv.0908.0278 · pith_short_12: HQFAVS72I2LN · pith_short_16: HQFAVS72I2LNHGOW · pith_short_8: HQFAVS72

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/HQFAVS72I2LNHGOWMQG5ROGE7D \
  | 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: 3c0a0acbfa4696d399d6640dd8b8c4f8c8491f781af044f8d28ef0c33e9732a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00c6f72b8f3cec2511821e528dfb010875942198fa5c5a3011d4620a307bc60f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2009-08-03T15:24:42Z",
    "title_canon_sha256": "529bb60bfa21530ec9eed816f239695f251fcd0f385607a288dfb15042caae57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.0278",
    "kind": "arxiv",
    "version": 3
  }
}