Pith Number

pith:DL2ABVD2

pith:2026:DL2ABVD2DJQ3QGEJ7UEMKXPKFT

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Analytic Bootstrap of the Veneziano Amplitude

Shi-Lin Wan, Shuang-Yong Zhou

The Veneziano amplitude is the unique outcome of an analytic bootstrap that uses dispersive sum rules, unitarity, and a minimal stringy condition.

arxiv:2605.11084 v2 · 2026-05-11 · hep-th

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Claims

C1strongest claim

We analytically prove, to all orders, that the Veneziano amplitude is the unique outcome of a dual bootstrap based on dispersive sum rules, unitarity, and a small amount of additional stringy input.

C2weakest assumption

That the chosen stringy input (monodromy condition or splitting and hidden-zero conditions) can be precisely incorporated into the amplitude ansatz in a way that renders the bootstrap sufficiently rigid to fix the amplitude uniquely, without additional assumptions or gaps in the moment interpretation of the sum rules.

C3one line summary

The Veneziano amplitude is the unique outcome of an analytic dual bootstrap from dispersive sum rules, unitarity, and either string monodromy or splitting and hidden-zero conditions.

Receipt and verification

First computed	2026-06-29T00:14:03.373108Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1af400d47a1a61b81889fd08c55dea2cf0c88437b8cc1d31a0038d30cddd8069

Aliases

arxiv: 2605.11084 · arxiv_version: 2605.11084v2 · doi: 10.48550/arxiv.2605.11084 · pith_short_12: DL2ABVD2DJQ3 · pith_short_16: DL2ABVD2DJQ3QGEJ · pith_short_8: DL2ABVD2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DL2ABVD2DJQ3QGEJ7UEMKXPKFT \
  | 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: 1af400d47a1a61b81889fd08c55dea2cf0c88437b8cc1d31a0038d30cddd8069

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40d6b464da720784facee80a92c076163057737f21286d21ae0ce5fd3ff19eac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-05-11T18:00:10Z",
    "title_canon_sha256": "d1998261522dd734b8d3a46193eb6d8e3cdc741e1394404df686cc886a19c698"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11084",
    "kind": "arxiv",
    "version": 2
  }
}