Pith Number

pith:F3R2UTVW

pith:2018:F3R2UTVWZE4RS3YWPM5YQZE6UU

not attested not anchored not stored refs pending

On the Discrepancy of Random Matrices with Many Columns

Cole Franks, Michael Saks

arxiv:1807.04318 v2 · 2018-07-11 · 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{F3R2UTVWZE4RS3YWPM5YQZE6UU}

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	2026-05-18T00:02:54.711501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ee3aa4eb6c939196f167b3b88649ea53d5d262d62a7c7aae615b9eea2d77a2b

Aliases

arxiv: 1807.04318 · arxiv_version: 1807.04318v2 · doi: 10.48550/arxiv.1807.04318 · pith_short_12: F3R2UTVWZE4R · pith_short_16: F3R2UTVWZE4RS3YW · pith_short_8: F3R2UTVW

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/F3R2UTVWZE4RS3YWPM5YQZE6UU \
  | 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: 2ee3aa4eb6c939196f167b3b88649ea53d5d262d62a7c7aae615b9eea2d77a2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f371952651fb50b0304b3fe90fb5d2d8ae0229b130557683b36928c002c7c5e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-07-11T19:23:17Z",
    "title_canon_sha256": "59bd3b0b070bdb3edceae8d71f5e65f3988f17332692f75b8351a05d29d4dfa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.04318",
    "kind": "arxiv",
    "version": 2
  }
}