Pith Number

pith:244QIN6J

pith:2016:244QIN6JOBYPQ5A4YFGAMWE3OO

not attested not anchored not stored refs pending

Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors

Tamar Ziegler, Terence Tao

arxiv:1603.07815 v4 · 2016-03-25 · math.CO · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{244QIN6JOBYPQ5A4YFGAMWE3OO}

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	2026-05-18T00:52:41.764446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7390437c97070f8741cc14c06589b7392732d98d8aeb2590eebb5d8adc58372

Aliases

arxiv: 1603.07815 · arxiv_version: 1603.07815v4 · doi: 10.48550/arxiv.1603.07815 · pith_short_12: 244QIN6JOBYP · pith_short_16: 244QIN6JOBYPQ5A4 · pith_short_8: 244QIN6J

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/244QIN6JOBYPQ5A4YFGAMWE3OO \
  | 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: d7390437c97070f8741cc14c06589b7392732d98d8aeb2590eebb5d8adc58372

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff234225e4cbddf08695b3796d77e0d896655e42cdf315f12ae19beb98c4932e",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-03-25T03:44:21Z",
    "title_canon_sha256": "65c3fd159459e0f65d64918de30f96436dae6a44da4321b095d4d66a81a8c1d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.07815",
    "kind": "arxiv",
    "version": 4
  }
}