Pith Number

pith:M5UNLSCX

pith:2014:M5UNLSCXLPB6ADXBHS7TJX7P6U

not attested not anchored not stored refs pending

Fibration theorem for Waldhausen K-theory

Satoshi Mochizuki

arxiv:1409.3637 v2 · 2014-09-12 · math.KT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M5UNLSCXLPB6ADXBHS7TJX7P6U}

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	2026-05-18T01:35:43.609461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6768d5c8575bc3e00ee13cbf34dfeff5379907d20a39a29bbd346140c36a183c

Aliases

arxiv: 1409.3637 · arxiv_version: 1409.3637v2 · doi: 10.48550/arxiv.1409.3637 · pith_short_12: M5UNLSCXLPB6 · pith_short_16: M5UNLSCXLPB6ADXB · pith_short_8: M5UNLSCX

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/M5UNLSCXLPB6ADXBHS7TJX7P6U \
  | 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: 6768d5c8575bc3e00ee13cbf34dfeff5379907d20a39a29bbd346140c36a183c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d66647c9c5344ac908e4263f808c22a8b22382ad617bd5f88b38ba424c9362b",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2014-09-12T02:33:35Z",
    "title_canon_sha256": "337201b94866881aa9fa15225d70b06705c317be7ca6116ad45b75064c75b900"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.3637",
    "kind": "arxiv",
    "version": 2
  }
}