Pith Number

pith:BWISSXTF

pith:2021:BWISSXTFZUMZF72X7HTD55XBK3

not attested not anchored not stored refs pending

Almost Sure Bounds for Discrepancies of Linear Forms on the Circle

Hao Wu

arxiv:2111.14981 v2 · 2021-11-29 · 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{BWISSXTFZUMZF72X7HTD55XBK3}

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	2026-06-08T01:03:39.674206Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d91295e65cd1992ff57f9e63ef6e156dcdbeb07927bd0fbc7c0ca3c1d6797ff

Aliases

arxiv: 2111.14981 · arxiv_version: 2111.14981v2 · doi: 10.48550/arxiv.2111.14981 · pith_short_12: BWISSXTFZUMZ · pith_short_16: BWISSXTFZUMZF72X · pith_short_8: BWISSXTF

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/BWISSXTFZUMZF72X7HTD55XBK3 \
  | 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: 0d91295e65cd1992ff57f9e63ef6e156dcdbeb07927bd0fbc7c0ca3c1d6797ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81294a6f583faff874598f927265fdac0a5a2cdf8409792a8093f92f46cd7112",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-11-29T21:51:24Z",
    "title_canon_sha256": "45df38ff5e6a4673eb812fb9dc99b8bee06e660c470ad4cce262b025a6dbf8c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.14981",
    "kind": "arxiv",
    "version": 2
  }
}