negbit

The Negbit Spec

An open quotation model for pre-processed knowledge bundles in machine-to-machine markets.

Version 1.0 · July 2026 · negbit.com · Nicolas Limare, ag3ntlab

This repository is the normative specification of the negbit pricing formula, its calibration defaults, the freshness rules, the domain half-life taxonomy, and the bundle audit protocol. The full derivation, the empirical calibration and the competitive analysis are in the white paper: read it online at negbit.com/paper or download the PDF.

Licensed CC BY-SA 4.0 (see License). The knowledge bundles you price with it remain entirely their owners' property.

---

1. What a negbit is

AI agents acquire task-relevant information two ways: by burning inference tokens to search, filter and synthesize raw sources, or by purchasing pre-processed, directly consumable context from another agent over machine-to-machine payment rails such as x402. A knowledge bundle is a curated set of text files built for agent consumption. A negbit is the unit this spec prices: one bundle of delivered negentropy, the ordering work that separates a curated bundle from the raw noise it was refined from.

The core claim of the model: the fair price of a bundle is the processing cost it saves its buyer, capped by what the answer is worth, decayed by the freshness of its domain, and split by bargaining weight.

2. The formula

The quote for a bundle of size $S$ tokens, age $a$ days, in a domain with half-life $t_{1/2}$ days:

$$ P^* ;=; \beta \cdot \min!\big[,\Delta \mathrm{EVSI},; C_{\mathrm{avoided}},\big] \cdot 2^{-a/t_{1/2}} $$

with a floor at the seller's amortized production cost per expected sale.

Terms:

Symbol	Meaning
$C_{\mathrm{avoided}}$	The processing cost the buyer skips by taking the bundle instead of doing the refinement work itself (expanded in §3)
$\Delta \mathrm{EVSI}$	The buyer's decision-theoretic value of the information (expected value of sample information); the cap that prevents pricing above what the answer is worth [1, 2]
$\beta$	Bargaining weight, the seller's share of the surplus; $\beta = 1/2$ is the symmetric Nash split [21]
$2^{-a/t_{1/2}}$	Freshness decay: the bundle's market value halves every domain half-life (see §4)

3. The avoided cost

$$ C_{\mathrm{avoided}} ;=; (1+r_{\mathrm{fail}})\big[, c_{\mathrm{in}},\rho,S ;+; c_{\mathrm{out}},\sigma,S ;+; c_{\mathrm{tool}},n ,\big] ;+; w,\Delta\tau ;-; c_{\mathrm{in}},S ;-; C_{\mathrm{verif}} $$

Reading it left to right: what the buyer would have spent reading the raw sources, synthesizing them, and paying for tool calls, inflated by the failure rate of autonomous research runs, plus the value of the time saved; minus the cost of reading the bundle itself and the cost of verifying the seller's claims.

The refinement ratio $\rho$ is the load-bearing quantity: how many raw tokens an agent would need to ingest per curated token delivered. Measured on real deep-research agent runs, honest values run 5 to 25 (raw dump ≈ 3, summarized ≈ 7, curated ≈ 15, deep-researched ≈ 25, expert distillation ≈ 35). $\rho$ is also where diffusion bites: knowledge that is ubiquitous and already well organized elsewhere has a collapsed effective $\rho$ regardless of how beautifully it is arranged. The formula prices the rarity of the refinement work, not the beauty of the order.

Calibration defaults (July 2026, from the paper §5)

Parameter	Default	Meaning
$c_{\mathrm{in}}$	$3 / Mtok	real-time input token price
$c_{\mathrm{out}}$	$15 / Mtok	output (synthesis) token price
$\rho$	15 (range 5–25)	refinement ratio
$\sigma$	2.5	synthesis output factor
$r_{\mathrm{fail}}$	0.3	failure/retry rate of autonomous runs
$c_{\mathrm{tool}} \cdot n$	$0.30	tool/search spend per run
$w,\Delta\tau$	$0.50	value of the latency saved
$C_{\mathrm{verif}}$	$0.05	buyer-side verification cost
$\beta$	0.5	Nash bargaining split
$t_{1/2}$	90 days	default half-life (overridden by taxonomy)
floor / cap	$0.05 / $5.00	one-shot quote guards

Worked example. $S = 10{,}000$ tokens, age 10 days, all defaults: $P^* = $0.87$ one-shot (sensitivity over $\rho \in [5, 25]$: $0.69 to $1.05). Calibrated one-shot quotes fall in $0.5–$4, independently consistent with observed x402 micropayment sizes (mean ≈ $0.20) [24, 25].

4. Freshness: the two decays

1. Obsolescence. The world drifts away from the bundle at the domain's pace. Value halves every $t_{1/2}$; maintenance resets the clock (the age is that of the last real content update, not of the file's creation). Genuinely timeless content is the limit $t_{1/2} \to \infty$.
2. Diffusion. As the same knowledge becomes freely and cleanly available elsewhere, the effective refinement ratio collapses, and the price with it [7]. Quality does not protect a commodity.

Fail-closed rule (normative): a bundle that does not declare a machine-readable last-update date (an updated: YYYY-MM-DD field in its index front matter) gets no quote at all until it does. A quoter must never invent a freshness date.

5. The half-life taxonomy

taxonomy.json maps 8 domains and 24 sub-domains to calibrated half-lives in days (v1, community-revisable under the license: from days for fast-moving software ecosystems to decades for settled foundations). A multi-domain bundle takes the smallest half-life among its dominant domains (conservative v1 rule).

6. The audit protocol

The normative procedure for auditing and quoting a bundle. Any conforming implementation follows six steps:

1. Scan and measure. Inventory the bundle; measure $S$ (text bytes / 4); note the presence of an index, a citation convention, and the updated: field.
2. Infer domain and half-life. From the content (never the folder name), pick the taxonomy's best domain / sub-domain pair; state the confidence.
3. Diagnose against the formula's terms. Each defect maps to a term, and the term gives its price impact: missing updated: is blocking (fail-closed); staleness burns the decay; thin coverage caps $S$ and $\Delta\mathrm{EVSI}$; raw dumps collapse $\rho$; missing provenance transfers $C_{\mathrm{verif}}$ to the buyer; ubiquity collapses effective $\rho$.
4. Produce a reconfiguration plan. Ordered, executable steps, each citing the term it improves.
5. Price deterministically. The quote comes from the formula with the declared inputs, never from a model's judgment. Same inputs, same price.
6. Report honestly. Price with its sensitivity range, domain with its confidence, and a plain statement when the content is commodity knowledge.

A reference implementation (the negbit-audit skill: the protocol as agent instructions plus a deterministic stdlib quoter) is distributed free against registration at negbit.com.

7. Conformance

An implementation conforms to this spec if it (a) computes the quote from §2–§3 with declared parameter values, (b) enforces the fail-closed freshness rule of §4, (c) resolves half-lives through §5 or a declared override, and (d) reports price as a point value with its $\rho$-sensitivity range. Derived taxonomies and calibrations must be shared under the same license (share-alike).

References

[1] R. A. Howard, "Information Value Theory," IEEE Transactions on Systems Science and Cybernetics 2(1), 22–26, 1966.

[2] H. Raiffa, R. Schlaifer, Applied Statistical Decision Theory, Harvard University, 1961.

[3] D. Blackwell, "Equivalent Comparisons of Experiments," Annals of Mathematical Statistics 24(2), 265–272, 1953.

[4] G. J. Stigler, "The Economics of Information," Journal of Political Economy 69(3), 213–225, 1961.

[5] K. J. Arrow, "Economic Welfare and the Allocation of Resources for Invention," in The Rate and Direction of Inventive Activity, NBER/Princeton, 609–626, 1962.

[6] C. Shapiro, H. R. Varian, Information Rules: A Strategic Guide to the Network Economy, Harvard Business School Press, 1999.

[7] S. J. Grossman, J. E. Stiglitz, "On the Impossibility of Informationally Efficient Markets," American Economic Review 70(3), 393–408, 1980.

[8] C. A. Sims, "Implications of Rational Inattention," Journal of Monetary Economics 50(3), 665–690, 2003.

[9] F. Matějka, A. McKay, "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review 105(1), 272–298, 2015.

[10] L. Szilard, "Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen," Zeitschrift für Physik 53, 840–856, 1929.

[11] L. Brillouin, "The Negentropy Principle of Information," Journal of Applied Physics 24(9), 1152–1163, 1953.

[12] R. Landauer, "Irreversibility and Heat Generation in the Computing Process," IBM Journal of Research and Development 5(3), 183–191, 1961.

[13] D. Bergemann, A. Bonatti, A. Smolin, "The Design and Price of Information," American Economic Review 108(1), 1–48, 2018.

[14] A. Agarwal, M. Dahleh, T. Sarkar, "A Marketplace for Data: An Algorithmic Solution," Proceedings of the 2019 ACM Conference on Economics and Computation (EC '19), 701–726, 2019.

[15] C. H. Bennett, "The Thermodynamics of Computation — a Review," International Journal of Theoretical Physics 21(12), 905–940, 1982.

[16] T. Sashihara et al., "LLM-based Multi-Agent System for Simulating Strategic and Goal-Oriented Data Marketplaces," arXiv:2511.13233, 2025.

[17] "Magentic Marketplace: An Open-Source Environment for Studying Agentic Markets," arXiv:2510.25779, 2025.

[18] "Agent Bazaar: Enabling Economic Alignment in Multi-Agent Marketplaces," arXiv:2605.17698, 2026.

[19] D. Bergemann, A. Bonatti, T. Gan, "The Economics of Social Data," RAND Journal of Economics 53(2), 263–296, 2022.

[20] Linux Foundation, "Launching the x402 Foundation," press release, 2026.

[21] J. F. Nash, "The Bargaining Problem," Econometrica 18(2), 155–162, 1950.

[22] Cloudflare, "Introducing Pay Per Crawl," July 2025; and the July 2026 transition to per-use compensation ("pay per use").

[23] Stanford Digital Economy Lab, "How are AI agents spending your tokens?", May 2026.

[24] CoinDesk / Artemis, "Coinbase-backed AI payments protocol wants to fix micropayments, but demand is just not there yet," March 2026.

[25] Coinbase Developer Platform, x402 documentation (facilitator pricing), accessed July 2026.

Citation

N. Limare, "Pricing Negentropy: A Quotation Model for Pre-Processed Context Bundles in Machine-to-Machine Knowledge Markets," ag3ntlab, v1.0, July 2026. negbit.com/paper

License

The Negbit Spec (this document, the formula, the audit protocol, and the taxonomy) is licensed under Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0). Attribution: negbit.com. The bundles you audit and price with it remain entirely their owners' property.