Pith Number

pith:5AONWHTG

pith:2015:5AONWHTGUMHFR2BRJXYFH42DT2

not attested not anchored not stored refs pending

The double shuffle relations for multiple Eisenstein series

Henrik Bachmann, Koji Tasaka

arxiv:1501.03408 v3 · 2015-01-14 · 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{5AONWHTGUMHFR2BRJXYFH42DT2}

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	2026-05-18T01:20:47.145135Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e81cdb1e66a30e58e8314df053f3439e81e74e49fb206948384b27173e9a7e65

Aliases

arxiv: 1501.03408 · arxiv_version: 1501.03408v3 · doi: 10.48550/arxiv.1501.03408 · pith_short_12: 5AONWHTGUMHF · pith_short_16: 5AONWHTGUMHFR2BR · pith_short_8: 5AONWHTG

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/5AONWHTGUMHFR2BRJXYFH42DT2 \
  | 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: e81cdb1e66a30e58e8314df053f3439e81e74e49fb206948384b27173e9a7e65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7ed8722ef27d7af486953ff178755fade6fb176e15e019385ad5b6a244209b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-01-14T16:56:50Z",
    "title_canon_sha256": "fc45e58c46b59a3c4ea3e33e41aea0bbb3af5a766748488b6eb12f4d718d8fbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.03408",
    "kind": "arxiv",
    "version": 3
  }
}