Pith Number

pith:YR4DSFWJ

pith:2016:YR4DSFWJ6LYRXCUBIERUJESD2Q

not attested not anchored not stored refs pending

Tilting modules and support $\tau$-tilting modules over preprojective algebras associated with symmetrizable Cartan matrices

Changjian Fu, Shengfei Geng

arxiv:1612.05867 v2 · 2016-12-18 · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YR4DSFWJ6LYRXCUBIERUJESD2Q}

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	2026-05-18T00:06:16.449396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4783916c9f2f11b8a814123449243d42d04da13915112595557800df8352721

Aliases

arxiv: 1612.05867 · arxiv_version: 1612.05867v2 · doi: 10.48550/arxiv.1612.05867 · pith_short_12: YR4DSFWJ6LYR · pith_short_16: YR4DSFWJ6LYRXCUB · pith_short_8: YR4DSFWJ

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/YR4DSFWJ6LYRXCUBIERUJESD2Q \
  | 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: c4783916c9f2f11b8a814123449243d42d04da13915112595557800df8352721

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b8a3c422c08c959209c908615b879c6fd4545e2028fe79a4928cb406b0a2f08",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2016-12-18T08:19:46Z",
    "title_canon_sha256": "bf095aa8906579fbe0a1f0f557dd748cb5decb061280cebe64a23e7d067aff44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05867",
    "kind": "arxiv",
    "version": 2
  }
}