Pith Number

pith:V4LMEIYW

pith:2015:V4LMEIYWXPVVR6E3ITFBZTJHSM

not attested not anchored not stored refs pending

The algebra of bi-brackets and regularised multiple Eisenstein series

Henrik Bachmann

arxiv:1504.08138 v1 · 2015-04-30 · 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{V4LMEIYWXPVVR6E3ITFBZTJHSM}

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	2026-05-18T02:17:23.213355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af16c22316bbeb58f89b44ca1ccd27930109713be82d9da46a3afb2e3d770217

Aliases

arxiv: 1504.08138 · arxiv_version: 1504.08138v1 · doi: 10.48550/arxiv.1504.08138 · pith_short_12: V4LMEIYWXPVV · pith_short_16: V4LMEIYWXPVVR6E3 · pith_short_8: V4LMEIYW

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/V4LMEIYWXPVVR6E3ITFBZTJHSM \
  | 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: af16c22316bbeb58f89b44ca1ccd27930109713be82d9da46a3afb2e3d770217

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e64f8290e101368707243da4c4e19877386c6e6c42d4c8147cf1795afb373c6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-04-30T09:31:12Z",
    "title_canon_sha256": "941767dd5363a791dcdf66c1334cb5daa8d201fe5dd49477f136355ff2e59763"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.08138",
    "kind": "arxiv",
    "version": 1
  }
}