Pith Number

pith:FB6EDS3S

pith:2015:FB6EDS3S7R3ER2T3UV5MKCKUKZ

not attested not anchored not stored refs pending

Symplectic displacement energy for exact Lagrangian immersions

Manabu Akaho

arxiv:1505.06560 v1 · 2015-05-25 · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FB6EDS3S7R3ER2T3UV5MKCKUKZ}

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	2026-05-18T02:03:44.609004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

287c41cb72fc7648ea7ba57ac5095456445b8a48290dfd77afd61341acae155a

Aliases

arxiv: 1505.06560 · arxiv_version: 1505.06560v1 · doi: 10.48550/arxiv.1505.06560 · pith_short_12: FB6EDS3S7R3E · pith_short_16: FB6EDS3S7R3ER2T3 · pith_short_8: FB6EDS3S

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/FB6EDS3S7R3ER2T3UV5MKCKUKZ \
  | 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: 287c41cb72fc7648ea7ba57ac5095456445b8a48290dfd77afd61341acae155a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec1e887c7b09d7a1ffb1bc58f5b12d1a06f288092471bf113345c67dece644e6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2015-05-25T08:16:56Z",
    "title_canon_sha256": "c238b8b6d2adb26c6f001c95f7a4b563c16d7f5cf117f1786f83a5e02af12b02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.06560",
    "kind": "arxiv",
    "version": 1
  }
}