Pith Number

pith:WS4XOMRN

pith:2016:WS4XOMRNEI4JU3TTBLWG3353EE

not attested not anchored not stored refs pending

Properness of nilprogressions and the persistence of polynomial growth of given degree

Matthew Tointon, Romain Tessera

arxiv:1612.05152 v5 · 2016-12-15 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WS4XOMRNEI4JU3TTBLWG3353EE}

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	2026-05-18T00:01:30.681342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4b977322d22389a6e730aec6defbb2115d6a3c74338c78adee7ad2ae9f224a1

Aliases

arxiv: 1612.05152 · arxiv_version: 1612.05152v5 · doi: 10.48550/arxiv.1612.05152 · pith_short_12: WS4XOMRNEI4J · pith_short_16: WS4XOMRNEI4JU3TT · pith_short_8: WS4XOMRN

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/WS4XOMRNEI4JU3TTBLWG3353EE \
  | 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: b4b977322d22389a6e730aec6defbb2115d6a3c74338c78adee7ad2ae9f224a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b91f3fcd12cf774788cf66567e20fef937b78084461e6bba1fd03a95e7b0616a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-12-15T17:32:04Z",
    "title_canon_sha256": "9ef917e64079a14063b237208b7921da9106a0fd303e3a1c58cf014a4692d762"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05152",
    "kind": "arxiv",
    "version": 5
  }
}