Pith Number

pith:FL3VBL4G

pith:2021:FL3VBL4G2A2OFUTO3U5Z7U4VCX

not attested not anchored not stored refs pending

Sobolev Inequalities and Convergence For Riemannian Metrics and Distance Functions

Brian Allen, Edward Bryden

arxiv:2112.05105 v2 · 2021-12-09 · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FL3VBL4G2A2OFUTO3U5Z7U4VCX}

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	2026-07-05T06:17:25.259305Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2af750af86d034e2d26edd3b9fd39515c35f86a1ab0a8db52a383b228d350b2f

Aliases

arxiv: 2112.05105 · arxiv_version: 2112.05105v2 · doi: 10.48550/arxiv.2112.05105 · pith_short_12: FL3VBL4G2A2O · pith_short_16: FL3VBL4G2A2OFUTO · pith_short_8: FL3VBL4G

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/FL3VBL4G2A2OFUTO3U5Z7U4VCX \
  | 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: 2af750af86d034e2d26edd3b9fd39515c35f86a1ab0a8db52a383b228d350b2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58525df318f9309b2a1a9ee4696839c4134ca335b77518e68ebcdb358b817b12",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-12-09T18:44:04Z",
    "title_canon_sha256": "3d5aef25b59e5c15345a77651a6fa6dcaf948edd61fbe2ceb0d854f4fdc30174"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.05105",
    "kind": "arxiv",
    "version": 2
  }
}