Pith Number

pith:DK64KWB4

pith:2014:DK64KWB4PIUGTKTY7NDDX5SABX

not attested not anchored not stored refs pending

On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field

Fumiya Amano, Masanori Morishita, Yasushi Mizusawa

arxiv:1412.6894 v5 · 2014-12-22 · math.NT · math.AT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DK64KWB4PIUGTKTY7NDDX5SABX}

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	2026-05-18T00:25:35.204342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1abdc5583c7a2869aa78fb463bf6400df998b53efa1ed15cc27fd8e1b5b0870a

Aliases

arxiv: 1412.6894 · arxiv_version: 1412.6894v5 · doi: 10.48550/arxiv.1412.6894 · pith_short_12: DK64KWB4PIUG · pith_short_16: DK64KWB4PIUGTKTY · pith_short_8: DK64KWB4

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/DK64KWB4PIUGTKTY7NDDX5SABX \
  | 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: 1abdc5583c7a2869aa78fb463bf6400df998b53efa1ed15cc27fd8e1b5b0870a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1fad84007a0d1d362c27ace0c5c002e615b03e30acb76bf8a47ebac5b1641aa",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-12-22T07:50:14Z",
    "title_canon_sha256": "a5f377a6982857313be2673266113d37e3c4609c0ee67e8317e2dd943492ddcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.6894",
    "kind": "arxiv",
    "version": 5
  }
}