Pith Number

pith:PN5GV7XA

pith:2015:PN5GV7XAHZJR4A6H4EQ4VRZKDU

not attested not anchored not stored refs pending

The Frobenius Condition, Right Properness, and Uniform Fibrations

Christian Sattler, Nicola Gambino

arxiv:1510.00669 v5 · 2015-10-02 · math.CT · math.AT · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PN5GV7XAHZJR4A6H4EQ4VRZKDU}

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	2026-05-18T00:34:10.590875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b7a6afee03e531e03c7e121cac72a1d3f9630bc41302e661f2f60bdb661a96a

Aliases

arxiv: 1510.00669 · arxiv_version: 1510.00669v5 · doi: 10.48550/arxiv.1510.00669 · pith_short_12: PN5GV7XAHZJR · pith_short_16: PN5GV7XAHZJR4A6H · pith_short_8: PN5GV7XA

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/PN5GV7XAHZJR4A6H4EQ4VRZKDU \
  | 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: 7b7a6afee03e531e03c7e121cac72a1d3f9630bc41302e661f2f60bdb661a96a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8dde0a321b1d79578b64605077c53cace48ca4c185c0e3f5551023c1035b910c",
    "cross_cats_sorted": [
      "math.AT",
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2015-10-02T18:11:46Z",
    "title_canon_sha256": "161aaa8e0627ed3e3224403e7ef83f22f3e1298e643ea3f9a44f96897cdce275"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.00669",
    "kind": "arxiv",
    "version": 5
  }
}