Pith Number

pith:3SQTYGO3

pith:2011:3SQTYGO3HZIIVSD7D5NP2VEB55

not attested not anchored not stored refs pending

On the concentration of certain additive functions

Dimitris Koukoulopoulos

arxiv:1111.1040 v4 · 2011-11-04 · 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{3SQTYGO3HZIIVSD7D5NP2VEB55}

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	2026-05-18T00:42:44.763759Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dca13c19db3e508ac87f1f5afd5481ef7135d1115ae4e937798d728688a25d59

Aliases

arxiv: 1111.1040 · arxiv_version: 1111.1040v4 · doi: 10.48550/arxiv.1111.1040 · pith_short_12: 3SQTYGO3HZII · pith_short_16: 3SQTYGO3HZIIVSD7 · pith_short_8: 3SQTYGO3

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/3SQTYGO3HZIIVSD7D5NP2VEB55 \
  | 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: dca13c19db3e508ac87f1f5afd5481ef7135d1115ae4e937798d728688a25d59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf608cad77ce45d7f0857c7836c45ba5194f9460a4830e5eed54956059c5b2cc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-11-04T04:44:57Z",
    "title_canon_sha256": "3cd7ff5c936485c42102d738a1915a58e5de72440ac910a3a6838a6bb52584da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1040",
    "kind": "arxiv",
    "version": 4
  }
}