Pith Number

pith:GUK2ZBYT

pith:2026:GUK2ZBYTFPACRBCLCKJISDIY6K

not attested not anchored not stored refs pending

$\tau$-tilting modules, depth and delooping level

Mingfei Xu, Xiaojin Zhang

arxiv:2606.11684 v1 · 2026-06-10 · math.RT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GUK2ZBYTFPACRBCLCKJISDIY6K}

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	2026-06-11T01:10:02.702072Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3515ac87132bc028844b1292890d18f2ac302932f3d7a68994d97b2191dd31ca

Aliases

arxiv: 2606.11684 · arxiv_version: 2606.11684v1 · doi: 10.48550/arxiv.2606.11684 · pith_short_12: GUK2ZBYTFPAC · pith_short_16: GUK2ZBYTFPACRBCL · pith_short_8: GUK2ZBYT

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/GUK2ZBYTFPACRBCLCKJISDIY6K \
  | 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: 3515ac87132bc028844b1292890d18f2ac302932f3d7a68994d97b2191dd31ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5583b3331d2dcf82fb394a0eeb4b0b5e428b982665f580cb83386cd5afebe0f5",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-06-10T05:53:54Z",
    "title_canon_sha256": "d67ce95988f61af1870f366b0c3709ed1232f5691fea054af6dd1551c46fabca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.11684",
    "kind": "arxiv",
    "version": 1
  }
}