Pith Number

pith:ACMROOCO

pith:2012:ACMROOCO7RUPOEJIDPQ77HNECE

not attested not anchored not stored refs pending

Quantization for an elliptic equation with critical exponential growth on compact Riemannian surface without boundary

Yunyan Yang

arxiv:1210.2807 v2 · 2012-10-10 · 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{ACMROOCO7RUPOEJIDPQ77HNECE}

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	2026-05-18T02:47:13.308398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

009917384efc68f711281be1ff9da4113318f4b8d910fd1d716d656c94c3a949

Aliases

arxiv: 1210.2807 · arxiv_version: 1210.2807v2 · doi: 10.48550/arxiv.1210.2807 · pith_short_12: ACMROOCO7RUP · pith_short_16: ACMROOCO7RUPOEJI · pith_short_8: ACMROOCO

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/ACMROOCO7RUPOEJIDPQ77HNECE \
  | 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: 009917384efc68f711281be1ff9da4113318f4b8d910fd1d716d656c94c3a949

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d10947614dd7a6fcdfa8329ea7f483c129a71c05779af17120f82ca3c10f22d",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-10-10T05:41:39Z",
    "title_canon_sha256": "2c9e8d2bcf24986b0332c25d6574a8b92fb315f3d75e791dadade617382e0533"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2807",
    "kind": "arxiv",
    "version": 2
  }
}