Pith Number

pith:XYIXFUPF

pith:2012:XYIXFUPFZBBVYGSLSWYVMKRVPL

not attested not anchored not stored refs pending

Coarsenings, injectives and Hom functors

Fred Rohrer

arxiv:1210.5325 v1 · 2012-10-19 · 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{XYIXFUPFZBBVYGSLSWYVMKRVPL}

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	2026-05-18T03:28:53.573389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be1172d1e5c8435c1a4b95b1562a357af2b243c70d53dc4c7f80eac795a7aed2

Aliases

arxiv: 1210.5325 · arxiv_version: 1210.5325v1 · doi: 10.48550/arxiv.1210.5325 · pith_short_12: XYIXFUPFZBBV · pith_short_16: XYIXFUPFZBBVYGSL · pith_short_8: XYIXFUPF

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/XYIXFUPFZBBVYGSLSWYVMKRVPL \
  | 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: be1172d1e5c8435c1a4b95b1562a357af2b243c70d53dc4c7f80eac795a7aed2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6565035569f63bdacedbaf1d248d6dec2747bf77600990c70bdaef20add5b090",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-10-19T06:38:08Z",
    "title_canon_sha256": "415d17bbbe01561c86cc6470e595f73e721a5368c8488730c07adf46b26a5b8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5325",
    "kind": "arxiv",
    "version": 1
  }
}