Pith Number

pith:MRPA4YNG

pith:2019:MRPA4YNGQO3RHXIMVMYOFN3O5R

not attested not anchored not stored refs pending

New Expander Bounds from Affine Group Energy

Audie Warren, Oliver Roche-Newton

arxiv:1905.03701 v1 · 2019-05-09 · 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{MRPA4YNGQO3RHXIMVMYOFN3O5R}

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	2026-05-17T23:46:36.966112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

645e0e61a683b713dd0cab30e2b76eec6ca5ab7844a082493233dd8fc3665ffa

Aliases

arxiv: 1905.03701 · arxiv_version: 1905.03701v1 · doi: 10.48550/arxiv.1905.03701 · pith_short_12: MRPA4YNGQO3R · pith_short_16: MRPA4YNGQO3RHXIM · pith_short_8: MRPA4YNG

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/MRPA4YNGQO3RHXIMVMYOFN3O5R \
  | 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: 645e0e61a683b713dd0cab30e2b76eec6ca5ab7844a082493233dd8fc3665ffa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bae4da84ff870594e97f56b5212ec793fa96aa5060f3a8affe23f0fba8b872be",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-05-09T15:46:51Z",
    "title_canon_sha256": "ecea8623d2974f2f53583e7e7a7e4af9474c6babfc216d90ec4cad7e92426eaa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.03701",
    "kind": "arxiv",
    "version": 1
  }
}