Pith Number

pith:VDGGTTK5

pith:2013:VDGGTTK5RYYZ4MILV3NKOOFJMS

not attested not anchored not stored refs pending

On the immersion classes of nearby Lagrangians

Mohammed Abouzaid, Thomas Kragh

arxiv:1305.6810 v3 · 2013-05-29 · math.SG · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDGGTTK5RYYZ4MILV3NKOOFJMS}

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	2026-05-18T00:44:29.778038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8cc69cd5d8e319e310baedaa738a96496de69599bd8974e4df2c26e688d4291

Aliases

arxiv: 1305.6810 · arxiv_version: 1305.6810v3 · doi: 10.48550/arxiv.1305.6810 · pith_short_12: VDGGTTK5RYYZ · pith_short_16: VDGGTTK5RYYZ4MIL · pith_short_8: VDGGTTK5

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/VDGGTTK5RYYZ4MILV3NKOOFJMS \
  | 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: a8cc69cd5d8e319e310baedaa738a96496de69599bd8974e4df2c26e688d4291

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6146a958ecbc79a828b963187d183eb848daf64e1cf8a46eac538ff7a69d0c31",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2013-05-29T14:13:52Z",
    "title_canon_sha256": "2589c06b3258d6d8b9474ebc2f4fdafd5cc9ef5bbd3d6ce8e559ca1b94f58cab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.6810",
    "kind": "arxiv",
    "version": 3
  }
}