Pith Number

pith:6NFDO6GW

pith:2011:6NFDO6GWDVMPJLFAOC7UXTW5RS

not attested not anchored not stored refs pending

Substitutions and 1/2-discrepancy of $\{n \theta + x\}$

David Ralston

arxiv:1105.5810 v1 · 2011-05-29 · 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{6NFDO6GWDVMPJLFAOC7UXTW5RS}

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	2026-05-18T04:21:01.480762Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f34a3778d61d58f4aca070bf4bcedd8ca6d95e41944c88f4ef9722ec7990b451

Aliases

arxiv: 1105.5810 · arxiv_version: 1105.5810v1 · doi: 10.48550/arxiv.1105.5810 · pith_short_12: 6NFDO6GWDVMP · pith_short_16: 6NFDO6GWDVMPJLFA · pith_short_8: 6NFDO6GW

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/6NFDO6GWDVMPJLFAOC7UXTW5RS \
  | 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: f34a3778d61d58f4aca070bf4bcedd8ca6d95e41944c88f4ef9722ec7990b451

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4aca9a7211f1079040aec0eee85ab901c1fa6c11897d34f67cc8bb777aab295",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-05-29T18:12:09Z",
    "title_canon_sha256": "5dca52829253374176b6f319b84e16794ddf9a206086751c38a0905c729a9246"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5810",
    "kind": "arxiv",
    "version": 1
  }
}