Pith Number

pith:T2QCKQBL

pith:2000:T2QCKQBLPWV2RIOE3KVPQ7DC3I

not attested not anchored not stored refs pending

Algebraic estimates, stability of local zeta functions, and uniform estimates for distribution functions

D. H. Phong, Jacob Sturm

arxiv:math/0007202 v1 · 2000-07-01 · 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{T2QCKQBLPWV2RIOE3KVPQ7DC3I}

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	2026-05-18T01:05:38.426010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ea025402b7daba8a1c4daaaf87c62da23eb8ed3dfe51b44e4e62bf5504d3ac9

Aliases

arxiv: math/0007202 · arxiv_version: math/0007202v1 · doi: 10.48550/arxiv.math/0007202 · pith_short_12: T2QCKQBLPWV2 · pith_short_16: T2QCKQBLPWV2RIOE · pith_short_8: T2QCKQBL

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/T2QCKQBLPWV2RIOE3KVPQ7DC3I \
  | 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: 9ea025402b7daba8a1c4daaaf87c62da23eb8ed3dfe51b44e4e62bf5504d3ac9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c4bf28cd1806d909444b650b3d1fdd07acbc18a75e08e58b981ebf0d1bcc291",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2000-07-01T00:00:00Z",
    "title_canon_sha256": "8b7f77224042284a4f3e7f6d54f8b07d0083f1842e06282bb2bfa31da149c17f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0007202",
    "kind": "arxiv",
    "version": 1
  }
}