Pith Number

pith:PPDTHECJ

pith:2025:PPDTHECJOWPUSQQ4LY46B6DUTP

not attested not anchored not stored refs pending

Low-degree mod 2 cohomology of classifying spaces of $G_2$-gauge groups

Dang Vo Phuc

arxiv:2512.12195 v4 · 2025-12-13 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PPDTHECJOWPUSQQ4LY46B6DUTP}

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	2026-05-29T02:05:38.360517Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bc7339049759f49421c5e39e0f8749bd385d0c80ae6a0ce5f4078072d7e19ee

Aliases

arxiv: 2512.12195 · arxiv_version: 2512.12195v4 · doi: 10.48550/arxiv.2512.12195 · pith_short_12: PPDTHECJOWPU · pith_short_16: PPDTHECJOWPUSQQ4 · pith_short_8: PPDTHECJ

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/PPDTHECJOWPUSQQ4LY46B6DUTP \
  | 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: 7bc7339049759f49421c5e39e0f8749bd385d0c80ae6a0ce5f4078072d7e19ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "425a2f5daab7622fbec2624ac9a75f7ffc7887ede52df579d6a13113e83e95b0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2025-12-13T05:50:49Z",
    "title_canon_sha256": "1d30baa755f3ac457a3868d81516e8b34e32d2c9a431f31a6bc514c977da1c82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.12195",
    "kind": "arxiv",
    "version": 4
  }
}