The Observatory

A living map of the finance-under-physical-constraint literature

36 works · 48 curated edges · 3 citations missing from the record · 10 since closed · 541 candidates in the curation queue · updated 2026-07-14

Economics & finance Physics Mathematics Law & policy Practice & grey 1950 1960 1970 1980 1990 2000 2010 2020 petrov-2025 cites wissner-gross-freer-2010 — In the MPRA reference list (verified 11 Jul 2026). lerner-2021 cites angel-2014 — Documented in the project record (publication conventions §9): the forward walk from Angel that would have surfaced Lerner on day one. cinque-2022-3459 cites ratanov-2007 — OpenAlex citation index (automated walk). cinque-2022-3459 cites kolesnik-ratanov-2013 — OpenAlex reference list (automated cross-check). cinque-2022-3459 cites kac-1974 — OpenAlex reference list (automated cross-check). cinque-2022-3459 cites goldstein-1951 — OpenAlex reference list (automated cross-check). carvalho-gaspar-2021 cites trzetrzelewski-2017 — OpenAlex reference list (automated cross-check). carvalho-gaspar-2021 cites haug-2004 — OpenAlex reference list (automated cross-check). carvalho-gaspar-2021 cites wissner-gross-freer-2010 — OpenAlex reference list (automated cross-check). carvalho-gaspar-2021 cites krugman-2010 — OpenAlex reference list (automated cross-check). carvalho-gaspar-2021 cites angel-2014 — OpenAlex reference list (automated cross-check). kolesnik-ratanov-2013 cites kac-1974 — OpenAlex reference list (automated cross-check). kolesnik-ratanov-2013 cites goldstein-1951 — OpenAlex reference list (automated cross-check). ratanov-2007 cites kac-1974 — OpenAlex reference list (automated cross-check). ratanov-2007 cites goldstein-1951 — OpenAlex reference list (automated cross-check). trzetrzelewski-2017 cites kac-1974 — OpenAlex reference list (automated cross-check). trzetrzelewski-2017 cites goldstein-1951 — OpenAlex reference list (automated cross-check). wissner-gross-freer-2010 cites ratanov-2007 — OpenAlex reference list (automated cross-check). wissner-gross-freer-2010 cites kac-1974 — OpenAlex reference list (automated cross-check). wissner-gross-freer-2010 cites goldstein-1951 — OpenAlex reference list (automated cross-check). gregorio-2021-8263 cites kolesnik-ratanov-2013 — OpenAlex citation index (automated walk). crescenzo-2018-0627 cites kolesnik-ratanov-2013 — OpenAlex citation index (automated walk). kolesnik-2017-0947 cites kolesnik-ratanov-2013 — OpenAlex citation index (automated walk). kolesnik-2014-4156 cites kolesnik-ratanov-2013 — OpenAlex citation index (automated walk). crescenzo-2018-0627 cites kac-1974 — OpenAlex reference list (automated cross-check). crescenzo-2018-0627 cites goldstein-1951 — OpenAlex reference list (automated cross-check). gregorio-2021-8263 cites kac-1974 — OpenAlex reference list (automated cross-check). gregorio-2021-8263 cites goldstein-1951 — OpenAlex reference list (automated cross-check). kolesnik-2014-4156 cites kac-1974 — OpenAlex reference list (automated cross-check). kolesnik-2014-4156 cites goldstein-1951 — OpenAlex reference list (automated cross-check). kolesnik-2017-0947 cites kac-1974 — OpenAlex reference list (automated cross-check). kolesnik-2017-0947 cites goldstein-1951 — OpenAlex reference list (automated cross-check). ratanov-2007 extends goldstein-1951 — Telegraph pricing built on the Goldstein–Kac finite-velocity process. ratanov-2007 extends kac-1974 — Telegraph pricing built on the Goldstein–Kac finite-velocity process. kolesnik-ratanov-2013 extends ratanov-2007 — Monograph consolidating the jump-telegraph pricing programme. petrov-2025 should cite angel-2014 — Petrov re-derives the regulatory consequences of light-speed information limits that Angel set out in 2014. Petrov's MPRA reference list (checked 11 Jul 2026) contains no Angel: two literatures solving the same problem without touching. petrov-2025 should cite krugman-2010 — Interplanetary market thought experiments with no reference to the founding interplanetary-trade analysis. No Krugman in the MPRA reference list (checked 11 Jul 2026). lerner-2021 should cite kabanov-stricker-2006 — Lerner models trading under transmission delay apparently unaware the fundamental theorem of asset pricing under delayed information existed as a named theorem fifteen years earlier. The map's type specimen: physics found the regulation strand but not the mathematics strand. since closed — cheah-wlsm-2025 should cite petrov-2025 — RCMH states the light-cone efficiency thesis months before the SpaceFi series. Series review lineage instruction (11 Jul 2026): acknowledge and position against it. since closed — cheah-wlsm-2025 should cite krugman-2010 — Series review lineage instruction (11 Jul 2026): the interplanetary framing has a founding text; anchor to it. since closed — cheah-wlsm-2025 should cite haug-2004 — Series review lineage instruction (11 Jul 2026): the term and the practitioner framing begin here. since closed — cheah-wlsm-2025 should cite wissner-gross-freer-2010 — Series review lineage instruction (11 Jul 2026): relativistic arbitrage geography precedes the framework and must be cited. since closed — cheah-wlsm-2025 should cite angel-2014 — Series review lineage instruction (11 Jul 2026): the regulatory agenda was set in 2014; 'first systematic treatment' claims are not defensible against it. since closed — cheah-rap1-2025 should cite kabanov-stricker-2006 — The causality-bounded pricing theorem is a light-cone specialisation of the FTAP under restricted information. Series review instruction (11 Jul 2026): anchor the theorem class. since closed — cheah-rap1-2025 should cite angel-2014 — RAP I's regulatory agenda substantially overlaps Angel's 2014 programme (project search log #4: high overlap). Cite and differentiate. since closed — cheah-rap-proofs-2025 should cite ratanov-2007 — Jump-telegraph martingale pricing anticipates the note's finite-velocity dynamics; the series review (11 Jul 2026) directs rebuilding on this foundation. since closed — cheah-rap-proofs-2025 should cite trzetrzelewski-2017 — A relativistic Black–Scholes with the classical limit already exists in the physics literature; the note must engage it. since closed — cheah-rap-proofs-2025 should cite kolesnik-ratanov-2013 — The telegraph pricing monograph is the strand's consolidated reference; the note's dynamics sit inside its subject matter. Epps, T.W. (1979). 'Comovements in Stock Prices in the Very Short Run'. Journal of the American Statistical Association 74(366). — The Epps effect: correlations decay as the horizon shrinks. The oldest empirical fingerprint of asynchronous information arrival. Epps 1979 Krugman, P. (2010 [1978]). 'The Theory of Interstellar Trade'. Economic Inquiry 48(4): 1119–1123. — Interest parity across reference frames travelling at relativistic speed. Founded the genre, and its credibility problem: serious analysis dressed as a joke. Krugman 2010 Budish, E., Cramton, P. & Shim, J. (2015). 'The High-Frequency Trading Arms Race: Frequent Batch Auctions as a Market Design Response'. Quarterly Journal of Economics 130(4). — Batch auctions as the market-design answer to the speed race. The terrestrial endpoint of latency economics: when speed is the problem, redesign time. Budish et al. 2015 Kirilenko, A. & Lamacie, G. (2015). 'Latency and Asset Prices'. SSRN 2546567. — Time-series evidence that latency moves prices. Stops one step short of the cross-sectional question: is latency a priced factor? Kirilenko–Lamacie 2015 Bloss & Kleinknecht (2016). SSRN 2716997. — Option valuation under relativistic time dilation. An early, isolated finance-side entry. Bloss–Kleinknecht 2016 Carvalho, V.H. & Gaspar, R.M. (2021). 'Relativistic Option Pricing'. International Journal of Financial Studies 9(2):32. — Special relativity applied to Black–Scholes when participants sit in different reference frames: maturity and volatility dilation, worked by finance academics rather than physicists. Carvalho–Gaspar 2021 Cheah, D. (2025). 'Relativistic Asset Pricing: Mathematical Proofs and Numerical Implementation'. SSRN 5721142. — The proofs-and-numerics companion to Part I. Revised July 2026. Cheah Proofs 2025 Cheah, D. (2025). 'Relativistic Asset Pricing: A Formal Treatment (Part I)'. SSRN 5693543. — The formal layer: causal filtrations, no-arbitrage under an information-velocity limit, arbitrage-reach bounds. Revised July 2026. Cheah RAP I 2025 Cheah, D. (2025). 'When Light-speed Matters: Rethinking Finance for Distributed Markets'. SSRN 5625790. — Extends market theory into regimes where communication delay is economically significant: light-cones replace synchronised time, causality bounds replace arbitrage bounds. The series' published thesis statement. Cheah WLSM 2025 Haug, E.G. (2004). 'Space-time Finance'. Wilmott Magazine. — Relativistic corrections to volatility-time, dilation and rates, written for working quants. The practitioner-facing origin of the term. Haug 2004 Wissner-Gross, A.D. & Freer, C.E. (2010). 'Relativistic Statistical Arbitrage'. Physical Review E 82:056104. — Light-speed limits make arbitrage a geography problem: optimal intermediate trading nodes between separated exchanges, mapped on a relativistic Earth. Wissner-Gross–Freer 2010 Laughlin, G., Aguirre, A. & Grundfest, J. (2014). 'Information Transmission between Financial Markets in Chicago and New York'. Financial Review 49(2): 283–312. — Measured the Chicago–New York microwave arms race converging on the light-speed bound. The empirical companion to the regulation debate in the same journal issue. Some index records add Michael Goldstein to the byline: he edited the issue, not the paper. Laughlin et al. 2014 Trzetrzelewski, M. (2017). 'The Relativistic Black–Scholes Model'. EPL 117: 38004. — Black–Scholes rebuilt on finite-velocity dynamics, recovering the classical model as c approaches infinity. The physics side of the telegraph-pricing bridge. Trzetrzelewski 2017 Lerner, P.B. (2021). 'Transmission of Trading Orders through Communication Line with Relativistic Delay'. International Journal of Financial Studies 9(1):12. — Queue theory for trading signals moving at finite velocity: the signal is distorted by trading along the line itself. Found the regulation strand (cites Angel); never found the mathematics strand. Lerner 2021 Abushaqra, M. (2025). 'Quantum Time Dilation in Financial Markets: A Relativistic Framework for High-Frequency Trading and Market Perception'. SSRN 5171309. — Quantum time dilation meets high-frequency trading. Slight overlap with the core programme, but its existence is the point: the field is crowding. Abushaqra 2025 Petrov, V. (2025). 'The Relativistic-Chaotic Market Hypothesis: On the Physical Impossibility of Perfect Informational Efficiency'. MPRA Paper 123835. — Light-cone bounds plus emergent chaos make perfect informational efficiency physically impossible, with interplanetary thought experiments. States the thesis months before the SpaceFi series. Cites Wissner-Gross & Freer; cites neither Angel nor Krugman. Petrov 2025 Goldstein, S. (1951). 'On Diffusion by Discontinuous Movements, and on the Telegraph Equation'. Quarterly Journal of Mechanics and Applied Mathematics 4(2). — The analytic root: diffusion with finite propagation speed, seventy years before anyone priced an option on it. Goldstein 1951 Kac, M. (1974). 'A Stochastic Model Related to the Telegrapher's Equation'. Rocky Mountain Journal of Mathematics 4(3). — The probabilistic root of the telegraph process (a 1956 lecture, printed 1974). Randomised direction-switching as a model of bounded-speed motion. Kac 1974 Boyle, P.P. & Emanuel, D. (1980). 'Discretely Adjusted Option Hedges'. Journal of Financial Economics 8(3). — Hedging error from discrete rebalancing: time granularity as a priced friction, decades before anyone called it latency. Boyle–Emanuel 1980 Kabanov, Y. & Stricker, C. (2006). 'The Dalang–Morton–Willinger Theorem Under Delayed and Restricted Information'. In Émery, M. & Yor, M. (eds), Séminaire de Probabilités XXXIX, Springer LNM 1874: 209–213. — The fundamental theorem of asset pricing under delayed and restricted information, proved as a named theorem. The result the physics entrants keep rediscovering without the machinery. Kabanov–Stricker 2006 Arriojas, M., Hu, Y., Mohammed, S.-E.A. & Pap, G. (2007). 'A Delayed Black and Scholes Formula'. Stochastic Analysis and Applications 25(2): 471–492. — Option pricing when the underlying carries its own delay: memory in the dynamics, priced. The mathematics the latency literature needed and mostly never found. Arriojas et al. 2007 Ratanov, N. (2007). 'A Jump Telegraph Model for Option Pricing'. Quantitative Finance 7(5): 575–583. — Arbitrage-free option pricing on finite-velocity dynamics via jump-telegraph martingale measures. The working core of the strand. Ratanov 2007 Kolesnik, A.D. & Ratanov, N. (2013). 'Telegraph Processes and Option Pricing'. Springer. — The monograph consolidating finite-velocity price dynamics: telegraph processes, equivalent martingale measures, option pricing. Kolesnik–Ratanov 2013 Alexander D. Kolesnik (2014). 'The explicit probability distribution of the sum of two telegraph processes'. Stochastics and Dynamics. — The paper derives closed-form expressions for the transition density and probability distribution function of the sum of two telegraph processes. Kolesnik 2014 Alexander D. Kolesnik (2017). 'Linear combinations of the telegraph random processes driven by partial differential equations'. Stochastics and Dynamics. — This work contributes a system of partial differential equations for the joint probability densities of linear combinations of independent telegraph random processes. Kolesnik 2017 Antonio Di Crescenzo, Alessandra Meoli (2018). 'On a jump-telegraph process driven by an alternating fractional Poisson process'. Journal of Applied Probability. — The authors develop a jump-telegraph process driven by a fractional alternating Poisson process with generalized Mittag-Leffler distributions. Crescenzo 2018 Alessandro De Gregorio, Francesco Iafrate (2021). 'Telegraph random evolutions on a circle'. IRIS Research product catalog (Sapienza University of Rome). — The paper contributes a stochastic model for the motion of a particle on a circle, generalizing the telegraph process to a circular domain. Gregorio 2021 Fabrizio Cinque (2022). 'Reflection principle for finite-velocity random motions'. Journal of Applied Probability. — The work contributes a reflection principle for a wide class of symmetric random motions with finite velocities. Fabrizio Cinque 2022 Mineiro, M.C. (2008). 'CISG and the Final Frontier'. SSRN 1285608; IISL proceedings. — Sale-of-goods law under space transit: passage of risk, the handing-over problem, damage known only after delay. A legal layer that has waited eighteen years for its finance layer. Mineiro 2008 Cape Town Convention Space Assets Protocol commentary: Sundahl; Hameed; HFW briefings. — The equipment-finance layer for space assets: registration, security interests, and why repossession doctrine breaks in orbit. Composite node; split into individual works as curation matures. Space Protocol comm. Angel, J.J. (2014). 'When Finance Meets Physics: The Impact of the Speed of Light on Financial Markets and Their Regulation'. Financial Review 49(2). — The regulatory agenda for light-speed markets, set out a decade early. The strand's anchor node, which later physics entrants keep failing to find. Index records sometimes show 'Angel & Goldstein': Goldstein edited the FR 49(2) issue; the paper is single-authored. Angel 2014 OSTP memorandum directing Coordinated Lunar Time (Apr 2024); NIST lunar timescale framework (Aug 2024). — The state building the timescale layer that any off-Earth market design will settle on. Policy infrastructure moving faster than the finance literature above it. OSTP/NIST LTC 2024 Tyc, S. (2015). McKay Brothers white paper on microwave latency. — Latency economics from the operator's desk: what a microsecond costs to buy and what it earns. The grey literature the academic strands price from. Tyc 2015 IEX Group — the 350-microsecond speed bump (exchange approval 2016). — Deliberately engineered latency as a fairness mechanism. The physical constraint used as a design tool rather than suffered as a cost. IEX 2016 Aon (quarterly) and WTW (annual) space insurance market reports. — Where physical risk in orbit actually gets priced today: premium volumes, loss ratios, capacity cycles. Data the theory strands never touch. Aon/WTW insurance 'Sniper in Mahwah' — pseudonymous blog by Alexandre Laumonier on HFT network geography. — Latency cartography of the exchange microwave networks, done from public records and antenna photographs. The field's unpaid surveyor. Sniper in Mahwah
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should cite (curated, justified) cites (documented) extends should-cite, since closed◦ ring = Space Finance Institute output

The missing edges

Citation-graph tools traverse the citations that exist. The defining feature of a disconnected literature is the citations that don't. Each entry below is a judgment that two works belong together, with the reason stated — the dashed amber lines on the map.

3 documented missing citations

Edges the record has closed

Gaps this map documented that have since been repaired — the record healing in response to its own diagnosis. The original justification stays on display; the map keeps score.

10 closed edges

The strands

Economics & finance (9)

Physics (7)

Mathematics (12)

Law & policy (4)

  • Mineiro, M.C. (2008). 'CISG and the Final Frontier'. SSRN 1285608; IISL proceedings.
    Sale-of-goods law under space transit: passage of risk, the handing-over problem, damage known only after delay. A legal layer that has waited eighteen years for its finance layer.
  • Cape Town Convention Space Assets Protocol commentary: Sundahl; Hameed; HFW briefings.
    The equipment-finance layer for space assets: registration, security interests, and why repossession doctrine breaks in orbit. Composite node; split into individual works as curation matures.
  • Angel, J.J. (2014). 'When Finance Meets Physics: The Impact of the Speed of Light on Financial Markets and Their Regulation'. Financial Review 49(2).
    The regulatory agenda for light-speed markets, set out a decade early. The strand's anchor node, which later physics entrants keep failing to find. Index records sometimes show 'Angel & Goldstein': Goldstein edited the FR 49(2) issue; the paper is single-authored.
  • OSTP memorandum directing Coordinated Lunar Time (Apr 2024); NIST lunar timescale framework (Aug 2024).
    The state building the timescale layer that any off-Earth market design will settle on. Policy infrastructure moving faster than the finance literature above it.

Practice & grey (4)

  • Tyc, S. (2015). McKay Brothers white paper on microwave latency.
    Latency economics from the operator's desk: what a microsecond costs to buy and what it earns. The grey literature the academic strands price from.
  • IEX Group — the 350-microsecond speed bump (exchange approval 2016).
    Deliberately engineered latency as a fairness mechanism. The physical constraint used as a design tool rather than suffered as a cost.
  • Aon (quarterly) and WTW (annual) space insurance market reports.
    Where physical risk in orbit actually gets priced today: premium volumes, loss ratios, capacity cycles. Data the theory strands never touch.
  • 'Sniper in Mahwah' — pseudonymous blog by Alexandre Laumonier on HFT network geography.
    Latency cartography of the exchange microwave networks, done from public records and antenna photographs. The field's unpaid surveyor.