Pith Number

pith:5X2QJDY5

pith:2016:5X2QJDY5H765C5RWOOEKWDS5YR

not attested not anchored not stored refs pending

On Garland's vanishing theorem for $\mathrm{SL}_n$

Mihran Papikian

arxiv:1612.07904 v1 · 2016-12-23 · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5X2QJDY5H765C5RWOOEKWDS5YR}

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	2026-05-18T00:54:05.384754Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edf5048f1d3ffdd176367388ab0e5dc44ea0e7632823bd968739863e770968f7

Aliases

arxiv: 1612.07904 · arxiv_version: 1612.07904v1 · doi: 10.48550/arxiv.1612.07904 · pith_short_12: 5X2QJDY5H765 · pith_short_16: 5X2QJDY5H765C5RW · pith_short_8: 5X2QJDY5

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/5X2QJDY5H765C5RWOOEKWDS5YR \
  | 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: edf5048f1d3ffdd176367388ab0e5dc44ea0e7632823bd968739863e770968f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bf54ef7db4c46f3accb4b6a9a7ace8fd12bb690ca0a59195f4d9f4d65e97e4c",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-23T08:37:11Z",
    "title_canon_sha256": "e568192b811ffb37ac0cbb6ed0096099a981c15f040dbd73e282c504a2a347c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.07904",
    "kind": "arxiv",
    "version": 1
  }
}