Pith Number

pith:VYD4YEHZ

pith:2011:VYD4YEHZCJK5XB4FKMQAVCUWGG

not attested not anchored not stored refs pending

Some critical point theorems and applications

Guangcun Lu

arxiv:1102.2136 v1 · 2011-02-10 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VYD4YEHZCJK5XB4FKMQAVCUWGG}

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	2026-05-18T04:29:34.174029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae07cc10f91255db878553200a8a9631ac0883e408b8d247b7f7b5836044f3f5

Aliases

arxiv: 1102.2136 · arxiv_version: 1102.2136v1 · doi: 10.48550/arxiv.1102.2136 · pith_short_12: VYD4YEHZCJK5 · pith_short_16: VYD4YEHZCJK5XB4F · pith_short_8: VYD4YEHZ

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/VYD4YEHZCJK5XB4FKMQAVCUWGG \
  | 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: ae07cc10f91255db878553200a8a9631ac0883e408b8d247b7f7b5836044f3f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5be688c73125dc38c8816cd1afd101b79951098ed6ccf0637136f1b79c38dc9a",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-02-10T14:56:58Z",
    "title_canon_sha256": "28c5ca88a868fb157f7c9fc85bed1f1577d6bac25eddfbace2fdee220eaa4047"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.2136",
    "kind": "arxiv",
    "version": 1
  }
}