Pith Number

pith:ZOP6XE4M

pith:2016:ZOP6XE4MM7I2BTZP5LY3ZHWGTL

not attested not anchored not stored refs pending

Phantom ideals and cotorsion pairs in extriangulated categories

Tiwei Zhao, Zhaoyong Huang

arxiv:1611.00477 v2 · 2016-11-02 · math.RT · 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{ZOP6XE4MM7I2BTZP5LY3ZHWGTL}

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	2026-05-18T00:50:51.923015Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb9feb938c67d1a0cf2feaf1bc9ec69acaf46ec42b53a7963361cb6e2480200b

Aliases

arxiv: 1611.00477 · arxiv_version: 1611.00477v2 · doi: 10.48550/arxiv.1611.00477 · pith_short_12: ZOP6XE4MM7I2 · pith_short_16: ZOP6XE4MM7I2BTZP · pith_short_8: ZOP6XE4M

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/ZOP6XE4MM7I2BTZP5LY3ZHWGTL \
  | 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: cb9feb938c67d1a0cf2feaf1bc9ec69acaf46ec42b53a7963361cb6e2480200b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "934e021e1534715532110aaf3b5abc99edac97c9d7645d8f023c78d6ada5aa44",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2016-11-02T05:51:43Z",
    "title_canon_sha256": "6aa188884c0114b7ee2f61b7aa66c368e7be4f978deb1adf81a3756173cc9a9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.00477",
    "kind": "arxiv",
    "version": 2
  }
}