Pith Number

pith:Y5JCVMV6

pith:2010:Y5JCVMV6BPN3AWWKYS2FIPXVCA

not attested not anchored not stored refs pending

Quasi-weak equivalences in complicial exact categories

Satoshi Mochizuki, Toshiro Hiranouchi

arxiv:1009.4608 v1 · 2010-09-23 · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y5JCVMV6BPN3AWWKYS2FIPXVCA}

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	2026-05-18T04:40:29.994222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7522ab2be0bdbb05acac4b4543ef5102dde4e2575ad0ad0618558320d8b6140

Aliases

arxiv: 1009.4608 · arxiv_version: 1009.4608v1 · doi: 10.48550/arxiv.1009.4608 · pith_short_12: Y5JCVMV6BPN3 · pith_short_16: Y5JCVMV6BPN3AWWK · pith_short_8: Y5JCVMV6

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/Y5JCVMV6BPN3AWWKYS2FIPXVCA \
  | 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: c7522ab2be0bdbb05acac4b4543ef5102dde4e2575ad0ad0618558320d8b6140

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3779d584eeb647e7af4fd11db9e6eb8fe57d1daa824f880b62877295c18e46dd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2010-09-23T13:22:20Z",
    "title_canon_sha256": "75d12d72d548d1a1018ce88a39b57f15005f921b1076803b65bcab74fea3d75c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4608",
    "kind": "arxiv",
    "version": 1
  }
}