Pith Number

pith:2EM4KV3L

pith:2009:2EM4KV3LXE5UNPC6GTDDJA2RAN

not attested not anchored not stored refs pending

Rack shadows and their invariants

Sam Nelson, Wesley Chang

arxiv:0910.3002 v2 · 2009-10-15 · math.GT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2EM4KV3LXE5UNPC6GTDDJA2RAN}

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	2026-07-04T17:31:36.493154Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d119c5576bb93b46bc5e34c63483510365fc7caf06ff518ec2dba458d4d67740

Aliases

arxiv: 0910.3002 · arxiv_version: 0910.3002v2 · doi: 10.48550/arxiv.0910.3002 · pith_short_12: 2EM4KV3LXE5U · pith_short_16: 2EM4KV3LXE5UNPC6 · pith_short_8: 2EM4KV3L

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/2EM4KV3LXE5UNPC6GTDDJA2RAN \
  | 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: d119c5576bb93b46bc5e34c63483510365fc7caf06ff518ec2dba458d4d67740

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f07404721428e105de93304b4c47b6cdd976a9413699692917d4f13274d14d3",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-10-15T21:36:56Z",
    "title_canon_sha256": "470511422ebb4f62629d5d440ff28273f2636c4f0957044d0f2ccae84d9582fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.3002",
    "kind": "arxiv",
    "version": 2
  }
}