Pith Number

pith:UNWWUTP3

pith:2013:UNWWUTP3QLJRVWK5CV5QVVRA67

not attested not anchored not stored refs pending

Subtle Invariants of $F$-crystals

Xiao Xiao

arxiv:1311.4009 v2 · 2013-11-16 · 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{UNWWUTP3QLJRVWK5CV5QVVRA67}

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	2026-05-18T02:38:37.332707Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a36d6a4dfb82d31ad95d157b0ad620f7d86a85947cbc7c7043ab555074f18637

Aliases

arxiv: 1311.4009 · arxiv_version: 1311.4009v2 · doi: 10.48550/arxiv.1311.4009 · pith_short_12: UNWWUTP3QLJR · pith_short_16: UNWWUTP3QLJRVWK5 · pith_short_8: UNWWUTP3

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/UNWWUTP3QLJRVWK5CV5QVVRA67 \
  | 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: a36d6a4dfb82d31ad95d157b0ad620f7d86a85947cbc7c7043ab555074f18637

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3dbe36dfa6f4896b710109b26fda486819ec09957c1b0ff1a989ac5bc6c197f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-16T01:50:43Z",
    "title_canon_sha256": "c84fee6e81cb1427966489c369f7b6677acf84371b9d1c39a426169a9187fe80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.4009",
    "kind": "arxiv",
    "version": 2
  }
}