Pith Number

pith:CM4GPOCV

pith:2015:CM4GPOCVZBNFO5VTOVCMDOMSHV

not attested not anchored not stored refs pending

Existence of compatible systems of lisse sheaves on arithmetic schemes

Koji Shimizu

arxiv:1509.05941 v2 · 2015-09-19 · 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{CM4GPOCVZBNFO5VTOVCMDOMSHV}

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	2026-05-18T00:51:37.838870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

133867b855c85a5776b37544c1b9923d71b496c67f848dee9bbb5b14f54bc37b

Aliases

arxiv: 1509.05941 · arxiv_version: 1509.05941v2 · doi: 10.48550/arxiv.1509.05941 · pith_short_12: CM4GPOCVZBNF · pith_short_16: CM4GPOCVZBNFO5VT · pith_short_8: CM4GPOCV

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/CM4GPOCVZBNFO5VTOVCMDOMSHV \
  | 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: 133867b855c85a5776b37544c1b9923d71b496c67f848dee9bbb5b14f54bc37b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36277dc02d89aca52a01dbf18cb2ea9c270e93a3b9ebd17a4441f2e8a1748953",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-09-19T22:08:39Z",
    "title_canon_sha256": "587af87567f7c74f914b49f39cc252ed52253a254e4129e1c5417629c644c407"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05941",
    "kind": "arxiv",
    "version": 2
  }
}