Pith Number

pith:YK4ML7JW

pith:2011:YK4ML7JWA25WSOGDRNFVMP6SYW

not attested not anchored not stored refs pending

Conformal invariants measuring the best constants for Gagliardo-Nirenberg-Sobolev inequalities

Jeffrey S. Case

arxiv:1112.3977 v1 · 2011-12-16 · 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{YK4ML7JWA25WSOGDRNFVMP6SYW}

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	2026-05-18T04:06:07.307227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2b8c5fd3606bb6938c38b4b563fd2c5af042703fd83e7c2901ddb5b3ac8a80b

Aliases

arxiv: 1112.3977 · arxiv_version: 1112.3977v1 · doi: 10.48550/arxiv.1112.3977 · pith_short_12: YK4ML7JWA25W · pith_short_16: YK4ML7JWA25WSOGD · pith_short_8: YK4ML7JW

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/YK4ML7JWA25WSOGDRNFVMP6SYW \
  | 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: c2b8c5fd3606bb6938c38b4b563fd2c5af042703fd83e7c2901ddb5b3ac8a80b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "646e4422c511c417c70f9f9abed8d40ff743a6efdbc6a05e7f6159630ea75bb9",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-12-16T21:38:42Z",
    "title_canon_sha256": "af01c40b9bf4adc5fbaa730f15f7a2b58e4adbf9c371311daf69c08e712820f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3977",
    "kind": "arxiv",
    "version": 1
  }
}