Pith Number

pith:ERBC6B5B

pith:2015:ERBC6B5BNDLW5VR7OFPJT2EDPN

not attested not anchored not stored refs pending

On the congruence $x^x\equiv \lambda \pmod p$

Javier Cilleruelo, Moubariz Z. Garaev

arxiv:1503.02730 v1 · 2015-03-09 · 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{ERBC6B5BNDLW5VR7OFPJT2EDPN}

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	2026-05-18T02:25:13.260100Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24422f07a168d76ed63f715e99e8837b6128323e84a2a56ed196252811e253f5

Aliases

arxiv: 1503.02730 · arxiv_version: 1503.02730v1 · doi: 10.48550/arxiv.1503.02730 · pith_short_12: ERBC6B5BNDLW · pith_short_16: ERBC6B5BNDLW5VR7 · pith_short_8: ERBC6B5B

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/ERBC6B5BNDLW5VR7OFPJT2EDPN \
  | 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: 24422f07a168d76ed63f715e99e8837b6128323e84a2a56ed196252811e253f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e93918356a8883fd0925f3b1020ed5eb69a5f1d87c27b4a076bea40371d9bb3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-03-09T23:23:03Z",
    "title_canon_sha256": "ca41f3e18647a7f5bcf9f32687e70cb3d865ecb469e572364a59a10d2747a58c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.02730",
    "kind": "arxiv",
    "version": 1
  }
}