Pith Number

pith:P4E4T4Q7

pith:2013:P4E4T4Q76JDT4VOIHIGPEGW4EO

not attested not anchored not stored refs pending

A proof of Grothendieck's base change theorem

Eduardo Tengan

arxiv:1312.7320 v1 · 2013-12-27 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P4E4T4Q76JDT4VOIHIGPEGW4EO}

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	2026-05-18T03:03:45.124369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f09c9f21ff2473e55c83a0cf21adc23872ecbe4fa5237f637db31727de29757

Aliases

arxiv: 1312.7320 · arxiv_version: 1312.7320v1 · doi: 10.48550/arxiv.1312.7320 · pith_short_12: P4E4T4Q76JDT · pith_short_16: P4E4T4Q76JDT4VOI · pith_short_8: P4E4T4Q7

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/P4E4T4Q76JDT4VOIHIGPEGW4EO \
  | 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: 7f09c9f21ff2473e55c83a0cf21adc23872ecbe4fa5237f637db31727de29757

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40417571ca05fb34962178de42da732b160b9f433728655abec0fae2b94d4aa2",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-12-27T19:39:21Z",
    "title_canon_sha256": "3883ef8c10fa48b7e4be46ef7e9da338d5728ae9749bf3c140fae7172a1d46cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7320",
    "kind": "arxiv",
    "version": 1
  }
}