Pith Number

pith:YPSW2V2H

pith:2026:YPSW2V2HWK3MQKQBMCGUNXPFQH

not attested not anchored not stored refs pending

Reduction modulo p of crystalline Galois representations via {\mu}_p-equivariance

Bhargav Bhatt, Mark Kisin, Toby Gee

arxiv:2607.08660 v1 · 2026-07-09 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YPSW2V2HWK3MQKQBMCGUNXPFQH}

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	2026-07-10T01:19:56.840236Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3e56d5747b2b6c82a01608d46dde581cd57fb62e792ee6bd06b8cd044c0fef2

Aliases

arxiv: 2607.08660 · arxiv_version: 2607.08660v1 · doi: 10.48550/arxiv.2607.08660 · pith_short_12: YPSW2V2HWK3M · pith_short_16: YPSW2V2HWK3MQKQB · pith_short_8: YPSW2V2H

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/YPSW2V2HWK3MQKQBMCGUNXPFQH \
  | 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: c3e56d5747b2b6c82a01608d46dde581cd57fb62e792ee6bd06b8cd044c0fef2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc4d705d25e12d368adfd53c620f4956552540874d6ca7889043ba61f901b434",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-09T16:28:13Z",
    "title_canon_sha256": "176ea9d1e635d54253b04ca14ba186ce6612ef04ba9eaaefb4a9657a75fac1de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08660",
    "kind": "arxiv",
    "version": 1
  }
}