Pith Number

pith:75IXQYPD

pith:2014:75IXQYPDBZ34UTBEH2DI54MZAR

not attested not anchored not stored refs pending

Additive dimension and a theorem of Sanders

Ilya D. Shkredov, Tomasz Schoen

arxiv:1404.2044 v1 · 2014-04-08 · math.CO · 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{75IXQYPDBZ34UTBEH2DI54MZAR}

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	2026-05-18T01:23:40.318067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff517861e30e77ca4c243e868ef1990473ead32451a359e0d1f59b9886486419

Aliases

arxiv: 1404.2044 · arxiv_version: 1404.2044v1 · doi: 10.48550/arxiv.1404.2044 · pith_short_12: 75IXQYPDBZ34 · pith_short_16: 75IXQYPDBZ34UTBE · pith_short_8: 75IXQYPD

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/75IXQYPDBZ34UTBEH2DI54MZAR \
  | 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: ff517861e30e77ca4c243e868ef1990473ead32451a359e0d1f59b9886486419

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06a227480b61e66122fe5fac7a93e529d3bf6c4dbec4f7799710a251fae0026b",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-04-08T08:49:39Z",
    "title_canon_sha256": "c0dd91bc2359458e9b7ed357d8299d65d498d27dc0cd855c217b0d37c4d43a4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.2044",
    "kind": "arxiv",
    "version": 1
  }
}