Pith Number

pith:XIZRBYLX

pith:2015:XIZRBYLXVOHVAUISP2VS3GTBU3

not attested not anchored not stored refs pending

Minimal $F$-crystals and isomorphism numbers of isosimple $F$-crystals

Xiao Xiao

arxiv:1509.01192 v2 · 2015-09-03 · 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{XIZRBYLXVOHVAUISP2VS3GTBU3}

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	2026-05-18T01:07:54.072118Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba3310e177ab8f5051127eab2d9a61a6cb7a4c9aa4e82cf7f628cb2505d261d1

Aliases

arxiv: 1509.01192 · arxiv_version: 1509.01192v2 · doi: 10.48550/arxiv.1509.01192 · pith_short_12: XIZRBYLXVOHV · pith_short_16: XIZRBYLXVOHVAUIS · pith_short_8: XIZRBYLX

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/XIZRBYLXVOHVAUISP2VS3GTBU3 \
  | 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: ba3310e177ab8f5051127eab2d9a61a6cb7a4c9aa4e82cf7f628cb2505d261d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0e40d2ad312da4b8e2953eddc069e4a4a5d4030fb593d8f2a8c8e48029b8d38",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-09-03T18:11:32Z",
    "title_canon_sha256": "95852feb0ecc43666f442c5b011227ee2c3409f82c3c806c73a2a2359b45abea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01192",
    "kind": "arxiv",
    "version": 2
  }
}