Pith Number

pith:57YZNK3A

pith:2005:57YZNK3A5YX3X5NI337YGUPX5Y

not attested not anchored not stored refs pending

A survey of tensor products and related constructions in two lectures

Friedrich Wehrung (LMNO), George Gr\"atzer

arxiv:math/0501416 v1 · 2005-01-24 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{57YZNK3A5YX3X5NI337YGUPX5Y}

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	2026-05-18T01:08:51.413175Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eff196ab60ee2fbbf5a8deff8351f7ee1097566b6eff377d817bec1a122ea522

Aliases

arxiv: math/0501416 · arxiv_version: math/0501416v1 · doi: 10.48550/arxiv.math/0501416 · pith_short_12: 57YZNK3A5YX3 · pith_short_16: 57YZNK3A5YX3X5NI · pith_short_8: 57YZNK3A

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/57YZNK3A5YX3X5NI337YGUPX5Y \
  | 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: eff196ab60ee2fbbf5a8deff8351f7ee1097566b6eff377d817bec1a122ea522

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47f3aded9ebd7ab7cd9280b3e34be0c3b9006ce240b35429535ff2cad29254de",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GM",
    "submitted_at": "2005-01-24T16:51:31Z",
    "title_canon_sha256": "1eb9ef03ae6ab49d1e543d96637096933a87b7843fb0037fcaeb2670f1775e00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0501416",
    "kind": "arxiv",
    "version": 1
  }
}