Pith Number

pith:R5MCQZX2

pith:2018:R5MCQZX2OQVAACNQLECKGACWZU

not attested not anchored not stored refs pending

Euler's Function on Products of Primes in Progressions

Amir Akbary, Forrest J. Francis

arxiv:1810.11524 v1 · 2018-10-26 · 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{R5MCQZX2OQVAACNQLECKGACWZU}

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	2026-05-18T00:02:08.400170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f582866fa742a0009b05904a30056cd06bc526de086af109e4401bdf52b34e4

Aliases

arxiv: 1810.11524 · arxiv_version: 1810.11524v1 · doi: 10.48550/arxiv.1810.11524 · pith_short_12: R5MCQZX2OQVA · pith_short_16: R5MCQZX2OQVAACNQ · pith_short_8: R5MCQZX2

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/R5MCQZX2OQVAACNQLECKGACWZU \
  | 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: 8f582866fa742a0009b05904a30056cd06bc526de086af109e4401bdf52b34e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5ebededdcde0d38e13690d70b1d014f20355f2a23798b00767234e94cc021b4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-10-26T20:39:30Z",
    "title_canon_sha256": "bd0f2f01615922ce0806e178755baa5dcd777c7a47074e23bedc45b238285c94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.11524",
    "kind": "arxiv",
    "version": 1
  }
}