Pith Number

pith:XHYEQ6SG

pith:2014:XHYEQ6SGDTZ2N2WM7VBPH2XJ65

not attested not anchored not stored refs pending

How many ways can you make change: Some easy proofs

William Gasarch

arxiv:1406.5213 v5 · 2014-06-19 · math.HO · 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{XHYEQ6SGDTZ2N2WM7VBPH2XJ65}

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	2026-05-18T02:47:15.188082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9f0487a461cf3a6eaccfd42f3eae9f741d841d714f5d1f864c7f43ae65b81db

Aliases

arxiv: 1406.5213 · arxiv_version: 1406.5213v5 · doi: 10.48550/arxiv.1406.5213 · pith_short_12: XHYEQ6SGDTZ2 · pith_short_16: XHYEQ6SGDTZ2N2WM · pith_short_8: XHYEQ6SG

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/XHYEQ6SGDTZ2N2WM7VBPH2XJ65 \
  | 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: b9f0487a461cf3a6eaccfd42f3eae9f741d841d714f5d1f864c7f43ae65b81db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4915b14447dbaf17c552bb12dacff6ed6055befbbe637d841e46733eaf063eb4",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2014-06-19T20:56:57Z",
    "title_canon_sha256": "ec293e5a96ddc55daeca9e852a405ca3fb1200bc7f7f763cf73633e1f7166c22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.5213",
    "kind": "arxiv",
    "version": 5
  }
}