Pith Number

pith:25VUXUPH

pith:2014:25VUXUPH4B6SW7Z3UQKDU3G25X

not attested not anchored not stored refs pending

Tensor product of dualizing complexes over a field

Liran Shaul

arxiv:1412.3759 v2 · 2014-12-11 · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{25VUXUPH4B6SW7Z3UQKDU3G25X}

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	2026-05-18T00:08:24.348855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d76b4bd1e7e07d2b7f3ba4143a6cdaedcc14ecd6e5585a001bee2cd944dd7579

Aliases

arxiv: 1412.3759 · arxiv_version: 1412.3759v2 · doi: 10.48550/arxiv.1412.3759 · pith_short_12: 25VUXUPH4B6S · pith_short_16: 25VUXUPH4B6SW7Z3 · pith_short_8: 25VUXUPH

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/25VUXUPH4B6SW7Z3UQKDU3G25X \
  | 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: d76b4bd1e7e07d2b7f3ba4143a6cdaedcc14ecd6e5585a001bee2cd944dd7579

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c9771514fee5299b75811d0ab8c3f028df0f89cb946114a2175ac52ab4055e2",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2014-12-11T18:51:21Z",
    "title_canon_sha256": "91570ae1dbf881599eb2978a481d456ae88d62dee3c6f73432fa1bd5c1b118f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.3759",
    "kind": "arxiv",
    "version": 2
  }
}