Pith Number

pith:ZPWXPHCK

pith:2015:ZPWXPHCKDYCYYDCTPOUGK5SEGE

not attested not anchored not stored refs pending

Lambda constant and Ground states of Perelman's W-functional

Li Ma

arxiv:1512.08405 v2 · 2015-12-28 · math.DG · 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{ZPWXPHCKDYCYYDCTPOUGK5SEGE}

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	2026-05-18T00:47:43.154380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbed779c4a1e058c0c537ba865764431208a2f374c66294f7c76085494d5280d

Aliases

arxiv: 1512.08405 · arxiv_version: 1512.08405v2 · doi: 10.48550/arxiv.1512.08405 · pith_short_12: ZPWXPHCKDYCY · pith_short_16: ZPWXPHCKDYCYYDCT · pith_short_8: ZPWXPHCK

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/ZPWXPHCKDYCYYDCTPOUGK5SEGE \
  | 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: cbed779c4a1e058c0c537ba865764431208a2f374c66294f7c76085494d5280d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e99de81527b4b52ca21732f41b71e462d351512169cc5428b5d5e7acdd202eea",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-12-28T13:15:08Z",
    "title_canon_sha256": "9d6c5d22427ae689a6d1c473cbdc7fee4bd4c01ebce36300ec75f69b7ef0f0c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08405",
    "kind": "arxiv",
    "version": 2
  }
}