Pith Number

pith:BR7N6NKP

pith:2016:BR7N6NKPZVPKVBONAYF2EATAJB

not attested not anchored not stored refs pending

An asymptotic formula for integer points on Markoff-Hurwitz varieties

Alex Gamburd, Michael Magee, Ryan Ronan

arxiv:1603.06267 v3 · 2016-03-20 · math.NT · math.DS · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BR7N6NKPZVPKVBONAYF2EATAJB}

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	2026-05-18T00:13:22.281398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c7edf354fcd5eaa85cd060ba202604844d6f88fd6b36aa8399d5e458e08cf02

Aliases

arxiv: 1603.06267 · arxiv_version: 1603.06267v3 · doi: 10.48550/arxiv.1603.06267 · pith_short_12: BR7N6NKPZVPK · pith_short_16: BR7N6NKPZVPKVBON · pith_short_8: BR7N6NKP

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/BR7N6NKPZVPKVBONAYF2EATAJB \
  | 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: 0c7edf354fcd5eaa85cd060ba202604844d6f88fd6b36aa8399d5e458e08cf02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f5f7c92671c21a1d5713f51351086da0a649d3a08bdb40b030114ef30ba0827",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-03-20T20:46:53Z",
    "title_canon_sha256": "6e9861ba745ebaa0d1726b10a915c58742ff0e8d00bf3f148b2c0e26f00073ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06267",
    "kind": "arxiv",
    "version": 3
  }
}