Pith Number

pith:ANTI4L2Y

pith:2015:ANTI4L2YHW3KA2ZFEJMYG2FCGG

not attested not anchored not stored refs pending

Currents carried by the subgradient graphs of semi-convex functions and applications to Hessian measure

Qiang Tu, Wenyi Chen

arxiv:1512.08850 v2 · 2015-12-30 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ANTI4L2YHW3KA2ZFEJMYG2FCGG}

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	2026-05-18T01:22:57.188534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03668e2f583db6a06b2522598368a231beb1b93fa148bbee34787be39ab119af

Aliases

arxiv: 1512.08850 · arxiv_version: 1512.08850v2 · doi: 10.48550/arxiv.1512.08850 · pith_short_12: ANTI4L2YHW3K · pith_short_16: ANTI4L2YHW3KA2ZF · pith_short_8: ANTI4L2Y

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/ANTI4L2YHW3KA2ZFEJMYG2FCGG \
  | 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: 03668e2f583db6a06b2522598368a231beb1b93fa148bbee34787be39ab119af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8967ed30a0dcd97c090488b25c6f5d7eb32b59383fc60f3df68add595267d1aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-12-30T05:04:19Z",
    "title_canon_sha256": "f30555a1d49f6d766640198f97632068d28712e8b49767ca064c5dffd1fea66a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08850",
    "kind": "arxiv",
    "version": 2
  }
}