Pith Number

pith:57SHS5EO

pith:2011:57SHS5EOX4NLHIBXQAJJMJK4AX

not attested not anchored not stored refs pending

The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus

Martin Kohlmann

arxiv:1107.3998 v2 · 2011-07-20 · 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{57SHS5EOX4NLHIBXQAJJMJK4AX}

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	2026-05-18T04:10:23.285096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efe479748ebf1ab3a037801296255c05ff7baebdf6f5786983a8c53bc752f320

Aliases

arxiv: 1107.3998 · arxiv_version: 1107.3998v2 · doi: 10.48550/arxiv.1107.3998 · pith_short_12: 57SHS5EOX4NL · pith_short_16: 57SHS5EOX4NLHIBX · pith_short_8: 57SHS5EO

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/57SHS5EOX4NLHIBXQAJJMJK4AX \
  | 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: efe479748ebf1ab3a037801296255c05ff7baebdf6f5786983a8c53bc752f320

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7fb09ab7b3fa8ef41ed49f9bb190284a7f7509c78bde56b4a3b7c7620b4461f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-07-20T15:09:12Z",
    "title_canon_sha256": "313aaf12e1f3c7136bbe2e019dab4147bfeda00446f1c2ef95f8e30424e23fdc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3998",
    "kind": "arxiv",
    "version": 2
  }
}