Pith Number

pith:UAEOEE5D

pith:2006:UAEOEE5DOF6FGKHM4BT7TN5R4K

not attested not anchored not stored refs pending

Congruence and Uniqueness of Certain Markoff Numbers

Ying Zhang

arxiv:math/0612620 v2 · 2006-12-20 · 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{UAEOEE5DOF6FGKHM4BT7TN5R4K}

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	2026-05-18T01:38:23.432273Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a008e213a3717c5328ece067f9b7b1e2964a83e29e22253ee31ca6f539c0f695

Aliases

arxiv: math/0612620 · arxiv_version: math/0612620v2 · doi: 10.48550/arxiv.math/0612620 · pith_short_12: UAEOEE5DOF6F · pith_short_16: UAEOEE5DOF6FGKHM · pith_short_8: UAEOEE5D

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/UAEOEE5DOF6FGKHM4BT7TN5R4K \
  | 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: a008e213a3717c5328ece067f9b7b1e2964a83e29e22253ee31ca6f539c0f695

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60c70802344b5499b939c4196c1feecb6656f2bef962e2cb32f11fc67cc8d559",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2006-12-20T20:19:21Z",
    "title_canon_sha256": "6458398fbf4b7e587c68ecc9b15ea37351541b10823f51c76283ce86524b6637"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612620",
    "kind": "arxiv",
    "version": 2
  }
}