Pith Number

pith:2HJDQDL4

pith:2021:2HJDQDL4MLUJJHGRJQ4ONPIFTR

not attested not anchored not stored refs pending

Equidistribution of expanding degenerate manifolds in the space of lattices

Nimish A. Shah, Pengyu Yang

arxiv:2112.13952 v4 · 2021-12-28 · math.DS · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2HJDQDL4MLUJJHGRJQ4ONPIFTR}

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	2026-06-09T01:05:02.206523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1d2380d7c62e8949cd14c38e6bd059c7d618b117425a4b14e9c742647f4f778

Aliases

arxiv: 2112.13952 · arxiv_version: 2112.13952v4 · doi: 10.48550/arxiv.2112.13952 · pith_short_12: 2HJDQDL4MLUJ · pith_short_16: 2HJDQDL4MLUJJHGR · pith_short_8: 2HJDQDL4

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/2HJDQDL4MLUJJHGRJQ4ONPIFTR \
  | 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: d1d2380d7c62e8949cd14c38e6bd059c7d618b117425a4b14e9c742647f4f778

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfd10ba6b6220240fead0386a21e2af4b2e628f670cdfcdaaad6e5de0b1570df",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2021-12-28T00:36:21Z",
    "title_canon_sha256": "de145d4a4d989ee664f68f8ced3984091cde93e3b72ca51b82ebaeadc19b42d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.13952",
    "kind": "arxiv",
    "version": 4
  }
}