Pith Number

pith:MDMPWYQE

pith:2026:MDMPWYQEMNTFCV6OSTEBMGVGKU

not attested not anchored not stored refs pending

From Grothendieck cofibrations to factorization systems: a formal 2-monadic account

Fernando Lucatelli Nunes, Walter Tholen

arxiv:2607.27541 v1 · 2026-07-30 · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MDMPWYQEMNTFCV6OSTEBMGVGKU}

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	2026-07-31T01:25:27.881608Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

60d8fb620463665157ce94c8161aa6551276891a56b5e079847d3be75271b23e

Aliases

arxiv: 2607.27541 · arxiv_version: 2607.27541v1 · doi: 10.48550/arxiv.2607.27541 · pith_short_12: MDMPWYQEMNTF · pith_short_16: MDMPWYQEMNTFCV6O · pith_short_8: MDMPWYQE

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/MDMPWYQEMNTFCV6OSTEBMGVGKU \
  | 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: 60d8fb620463665157ce94c8161aa6551276891a56b5e079847d3be75271b23e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7a9fb57695ccd5ba022e06a35795b8336f0de4828f7a3a3f060c89c92463030",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-07-30T00:22:45Z",
    "title_canon_sha256": "a89606dd1da842a2308f454562d3204556bf9b809420eb332b21507d3ba05579"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27541",
    "kind": "arxiv",
    "version": 1
  }
}