Pith Number

pith:UPEEVTYG

pith:2010:UPEEVTYGRNSGQFH63H6ZTAK3G2

not attested not anchored not stored refs pending

On common values of $\phi(n)$ and $\sigma(m)$, II

Kevin Ford, Paul Pollack

arxiv:1012.0080 v1 · 2010-12-01 · 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{UPEEVTYGRNSGQFH63H6ZTAK3G2}

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	2026-05-18T02:55:57.771376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3c84acf068b646814fed9fd99815b368e2ee2f5167bcb2fbf5111dbf0bd86f1

Aliases

arxiv: 1012.0080 · arxiv_version: 1012.0080v1 · doi: 10.48550/arxiv.1012.0080 · pith_short_12: UPEEVTYGRNSG · pith_short_16: UPEEVTYGRNSGQFH6 · pith_short_8: UPEEVTYG

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/UPEEVTYGRNSGQFH63H6ZTAK3G2 \
  | 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: a3c84acf068b646814fed9fd99815b368e2ee2f5167bcb2fbf5111dbf0bd86f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6bf3afa4a067543be248c12db3e4f79d7cdd92c7d64586d8104912617c180dcc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-12-01T02:03:58Z",
    "title_canon_sha256": "3feb399c5576399b44d462873a07219e6bdf078f09772e1b7120e901321eff00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0080",
    "kind": "arxiv",
    "version": 1
  }
}