Pith Number

pith:WK7AIJCY

pith:2007:WK7AIJCY2KMJVXDDQF7UBJFL22

not attested not anchored not stored refs pending

Entropy Functionals, Sobolev Inequalities and kappa-Noncollapsing Estimates along the Ricci Flow

Rugang Ye

arxiv:0709.2724 v1 · 2007-09-18 · 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{WK7AIJCY2KMJVXDDQF7UBJFL22}

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	2026-07-04T15:04:20.318925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2be042458d2989adc63817f40a4abd6aff51054975fa7897f6db23e5e2322b4

Aliases

arxiv: 0709.2724 · arxiv_version: 0709.2724v1 · doi: 10.48550/arxiv.0709.2724 · pith_short_12: WK7AIJCY2KMJ · pith_short_16: WK7AIJCY2KMJVXDD · pith_short_8: WK7AIJCY

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/WK7AIJCY2KMJVXDDQF7UBJFL22 \
  | 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: b2be042458d2989adc63817f40a4abd6aff51054975fa7897f6db23e5e2322b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fb995458b5037492106dfd097c8e3c7fca7560df38ed2b10e2183666094c601",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2007-09-18T19:57:23Z",
    "title_canon_sha256": "68b5d1f4c89083a811093b27b2376f58024dbd57482623824d01524fe9e8581a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.2724",
    "kind": "arxiv",
    "version": 1
  }
}