Pith Number

pith:VX2OCPIU

pith:2012:VX2OCPIUNMPXYRECK5MPBWEFDI

not attested not anchored not stored refs pending

Embedding functors and their arithmetic properties

Ting-Yu Lee

arxiv:1211.3564 v2 · 2012-11-15 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VX2OCPIUNMPXYRECK5MPBWEFDI}

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	2026-05-18T03:27:32.444173Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adf4e13d146b1f7c44825758f0d8851a2af442823035daa0a2888b6570dd172f

Aliases

arxiv: 1211.3564 · arxiv_version: 1211.3564v2 · doi: 10.48550/arxiv.1211.3564 · pith_short_12: VX2OCPIUNMPX · pith_short_16: VX2OCPIUNMPXYREC · pith_short_8: VX2OCPIU

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/VX2OCPIUNMPXYRECK5MPBWEFDI \
  | 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: adf4e13d146b1f7c44825758f0d8851a2af442823035daa0a2888b6570dd172f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4cbfe4ec12042d49510942cad86bc02e89486126cc74c417e2579262a4461ada",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-11-15T10:28:38Z",
    "title_canon_sha256": "aabf6d4016cc45b9f7c7db779dc18680975277e93d2797d84226f69953dc693e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3564",
    "kind": "arxiv",
    "version": 2
  }
}