Pith Number

pith:VWP7VD3H

pith:2011:VWP7VD3HCGHWXL2CJPC7I3PIT6

not attested not anchored not stored refs pending

Moduli Spaces and Grassmannian

Albert Schwarz, Jia-Ming Liou

arxiv:1111.1649 v4 · 2011-11-07 · math-ph · math.AG · math.AT · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VWP7VD3HCGHWXL2CJPC7I3PIT6}

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	2026-05-18T03:58:04.352474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad9ffa8f67118f6baf424bc5f46de89f8b29dbbe05c10191911dde0127fafff8

Aliases

arxiv: 1111.1649 · arxiv_version: 1111.1649v4 · doi: 10.48550/arxiv.1111.1649 · pith_short_12: VWP7VD3HCGHW · pith_short_16: VWP7VD3HCGHWXL2C · pith_short_8: VWP7VD3H

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/VWP7VD3HCGHWXL2CJPC7I3PIT6 \
  | 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: ad9ffa8f67118f6baf424bc5f46de89f8b29dbbe05c10191911dde0127fafff8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4200d8f1bb493215938ba23f210e06e6caa77c7c0cf5318a5c40a12283af56b2",
    "cross_cats_sorted": [
      "math.AG",
      "math.AT",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-11-07T17:21:51Z",
    "title_canon_sha256": "b41c7482eef60d8f70f194728c559c00f0c2c6e59baf992a80d873997db58e53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1649",
    "kind": "arxiv",
    "version": 4
  }
}