Pith Number

pith:TQYGXT5B

pith:2015:TQYGXT5B24AL3R2ZKNQYIK2MQ2

not attested not anchored not stored refs pending

Growth Estimates in Positive Characteristic via Collisions

Brendan Murphy, Esen Aksoy Yazici, Ilya Shkredov, Misha Rudnev

arxiv:1512.06613 v1 · 2015-12-21 · 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{TQYGXT5B24AL3R2ZKNQYIK2MQ2}

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	2026-05-18T01:24:00.034725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c306bcfa1d700bdc7595361842b4c86ae5efc35fb14cefa2bbfc36529841bd4

Aliases

arxiv: 1512.06613 · arxiv_version: 1512.06613v1 · doi: 10.48550/arxiv.1512.06613 · pith_short_12: TQYGXT5B24AL · pith_short_16: TQYGXT5B24AL3R2Z · pith_short_8: TQYGXT5B

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/TQYGXT5B24AL3R2ZKNQYIK2MQ2 \
  | 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: 9c306bcfa1d700bdc7595361842b4c86ae5efc35fb14cefa2bbfc36529841bd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "738b36d10acd8a4dffe6b922bc34bb22656bf49e1b407b2f40da90d732772c1b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-21T13:12:24Z",
    "title_canon_sha256": "2c47d14bd673055ee2c735a7adfdb5b4ca6fb20da0be0c0346ba0b4a15c0d4a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06613",
    "kind": "arxiv",
    "version": 1
  }
}