Pith Number

pith:X3ESPXOL

pith:2011:X3ESPXOLQVQNPGIBUNFLMLIUKR

not attested not anchored not stored refs pending

Counting Fixed Points, Two-Cycles, and Collisions of the Discrete Exponential Function using p-adic Methods

Joshua Holden, Margaret M. Robinson

arxiv:1105.5346 v1 · 2011-05-26 · math.NT · cs.CR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X3ESPXOLQVQNPGIBUNFLMLIUKR}

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	2026-05-18T03:39:29.347045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bec927ddcb8560d79901a34ab62d14546da047bc6400fdbd0ab1df1052d0e9b2

Aliases

arxiv: 1105.5346 · arxiv_version: 1105.5346v1 · doi: 10.48550/arxiv.1105.5346 · pith_short_12: X3ESPXOLQVQN · pith_short_16: X3ESPXOLQVQNPGIB · pith_short_8: X3ESPXOL

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/X3ESPXOLQVQNPGIBUNFLMLIUKR \
  | 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: bec927ddcb8560d79901a34ab62d14546da047bc6400fdbd0ab1df1052d0e9b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14c48de067a1ff98c8c1ddbd0703e006452f931cd64b24782873dec8fceb6c45",
    "cross_cats_sorted": [
      "cs.CR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-05-26T16:46:57Z",
    "title_canon_sha256": "a60f0cb20282364570529ae5d08724f9fd25c7b3bc30cbb05fb6a3c6356b1ac1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5346",
    "kind": "arxiv",
    "version": 1
  }
}