Pith Number

pith:JNFU4OPP

pith:2015:JNFU4OPPQTY2UYLC3R27Q77BA4

not attested not anchored not stored refs pending

Potentially crystalline deformation rings and Serre weight conjectures

Bao V. Le Hung, Brandon Levin, Daniel Le, Stefano Morra

arxiv:1512.06380 v3 · 2015-12-20 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JNFU4OPPQTY2UYLC3R27Q77BA4}

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	2026-05-18T00:31:52.195614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b4b4e39ef84f1aa6162dc75f87fe10715f3540ff775687b02883051daf4cdf3

Aliases

arxiv: 1512.06380 · arxiv_version: 1512.06380v3 · doi: 10.48550/arxiv.1512.06380 · pith_short_12: JNFU4OPPQTY2 · pith_short_16: JNFU4OPPQTY2UYLC · pith_short_8: JNFU4OPP

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/JNFU4OPPQTY2UYLC3R27Q77BA4 \
  | 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: 4b4b4e39ef84f1aa6162dc75f87fe10715f3540ff775687b02883051daf4cdf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8d616356627e5feeb567a0d891ceff186930f3d853e1cfeeddaff57c33a84fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-12-20T15:27:09Z",
    "title_canon_sha256": "cc7724fa335e0dc9e4da19c550b7f7161e14029b04a54c6d171247dbf93612e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06380",
    "kind": "arxiv",
    "version": 3
  }
}