Pith Number

pith:PCKWK2MF

pith:2015:PCKWK2MFIVBYX3ZQU7B7PAK7SG

not attested not anchored not stored refs pending

Explicit computations of Hida families via overconvergent modular symbols

Daniel Ross, Evan P. Dummit, Lalit Jain, M\'arton Hablicsek, Robert Harron, Robert Pollack

arxiv:1510.05795 v2 · 2015-10-20 · 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{PCKWK2MFIVBYX3ZQU7B7PAK7SG}

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	2026-05-18T01:09:36.412268Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

789565698545438bef30a7c3f7815f91b4601f884bf82858348678b74b9d630a

Aliases

arxiv: 1510.05795 · arxiv_version: 1510.05795v2 · doi: 10.48550/arxiv.1510.05795 · pith_short_12: PCKWK2MFIVBY · pith_short_16: PCKWK2MFIVBYX3ZQ · pith_short_8: PCKWK2MF

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/PCKWK2MFIVBYX3ZQU7B7PAK7SG \
  | 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: 789565698545438bef30a7c3f7815f91b4601f884bf82858348678b74b9d630a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "361340429a9222dc35272dc61b141d7d0adf4be92c6abd7ca85834c09cfaacc5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-10-20T08:56:13Z",
    "title_canon_sha256": "819c22d12a8328a76bc88a832ac01dcc27452c7013661d4ecf8bce32f41d5928"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05795",
    "kind": "arxiv",
    "version": 2
  }
}