Pith Number

pith:76D7EDQD

pith:2017:76D7EDQDMHTQEEJYK4ZHAXG54H

not attested not anchored not stored refs pending

Linear stable range for homology of congruence subgroups via FI-modules

Liping Li, Wee Liang Gan

arxiv:1712.00890 v2 · 2017-12-04 · math.RT · math.AT · math.KT · 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{76D7EDQDMHTQEEJYK4ZHAXG54H}

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	2026-07-04T23:59:14.358242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff87f20e0361e70211385732705cdde1e067fd6004090926c0f2d44a2c62ba70

Aliases

arxiv: 1712.00890 · arxiv_version: 1712.00890v2 · doi: 10.48550/arxiv.1712.00890 · pith_short_12: 76D7EDQDMHTQ · pith_short_16: 76D7EDQDMHTQEEJY · pith_short_8: 76D7EDQD

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/76D7EDQDMHTQEEJYK4ZHAXG54H \
  | 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: ff87f20e0361e70211385732705cdde1e067fd6004090926c0f2d44a2c62ba70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57df5882afa90fda571311c0ad58e87714b402b355eb2a473cd01da1bb57d815",
    "cross_cats_sorted": [
      "math.AT",
      "math.KT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2017-12-04T03:28:38Z",
    "title_canon_sha256": "423dcb0f36f443e0158d3f4ce646d95375affa93202428a1b50d7542b19b21ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.00890",
    "kind": "arxiv",
    "version": 2
  }
}