Pith Number

pith:6CMIIX2F

pith:2012:6CMIIX2F7D5IQ4SYLO4BQG7VA4

not attested not anchored not stored refs pending

Birationality of Berglund-H\"ubsch-Krawitz Mirrors

Mark Shoemaker

arxiv:1209.5016 v2 · 2012-09-22 · math.AG · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6CMIIX2F7D5IQ4SYLO4BQG7VA4}

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	2026-05-18T01:23:31.738879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f098845f45f8fa8872585bb8181bf50730e2fa7ed605afd9f4cf1b0d1b2e4045

Aliases

arxiv: 1209.5016 · arxiv_version: 1209.5016v2 · doi: 10.48550/arxiv.1209.5016 · pith_short_12: 6CMIIX2F7D5I · pith_short_16: 6CMIIX2F7D5IQ4SY · pith_short_8: 6CMIIX2F

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/6CMIIX2F7D5IQ4SYLO4BQG7VA4 \
  | 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: f098845f45f8fa8872585bb8181bf50730e2fa7ed605afd9f4cf1b0d1b2e4045

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e491a2e7685efcc98bb4d1254925bddea6aaa2965fb0d0cbe3b8c6bac5f1be7b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-09-22T19:17:20Z",
    "title_canon_sha256": "55e658c8f85ec207a61e9e5302101018163354df2141e2591fbe710f0a883d81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5016",
    "kind": "arxiv",
    "version": 2
  }
}