Pith Number

pith:ULLXDUIR

pith:2016:ULLXDUIRFX6MB5G2SBNO5JYMFA

not attested not anchored not stored refs pending

Oddness of residually reducible Galois representations

Tobias Berger

arxiv:1611.09315 v1 · 2016-11-28 · 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{ULLXDUIRFX6MB5G2SBNO5JYMFA}

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	2026-05-18T00:56:28.547305Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2d771d1112dfcc0f4da905aeea70c28278af8e922536d842fe52cafad1504b5

Aliases

arxiv: 1611.09315 · arxiv_version: 1611.09315v1 · doi: 10.48550/arxiv.1611.09315 · pith_short_12: ULLXDUIRFX6M · pith_short_16: ULLXDUIRFX6MB5G2 · pith_short_8: ULLXDUIR

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/ULLXDUIRFX6MB5G2SBNO5JYMFA \
  | 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: a2d771d1112dfcc0f4da905aeea70c28278af8e922536d842fe52cafad1504b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fbd505a06705c14539acb6c7a48d7c2ed993aeb25a3dda529de3902d88113a2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-11-28T20:05:53Z",
    "title_canon_sha256": "923dab89bcabf9f2af420c9e5fb3eb3f8160c1eceac9e2d95bdcf5639128fae6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.09315",
    "kind": "arxiv",
    "version": 1
  }
}